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Deck 17: Second-Order Differential Equations
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Question
Suppose a spring has mass M and spring constant k and let 
. Suppose that the damping constant is so small that the damping force is negligible. If an external force 
is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.
A)
B)
C)
D)
E)
. Suppose that the damping constant is so small that the damping force is negligible. If an external force is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.A)
B)
C)
D)
E)
Question
A series circuit consists of a resistor 
, an inductor with 
, a capacitor with 
, and a 
-V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.
A)
B)
C)
D)
E)
, an inductor with , a capacitor with , and a -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.A)
B)
C)
D)
E)
Question
A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of 
m/s, find the position x(t) of the mass after t seconds.
A)
B)
C)
D)
E)
m/s, find the position x(t) of the mass after t seconds.A)
B)
C)
D)
E)
Question
Use power series to solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use power series to solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A spring with a mass of 2 kg has damping constant 14, and a force of 
N is required to keep the spring stretched 
m beyond its natural length. The spring is stretched 1m beyond its natural length and then released with zero velocity. Find the position x(t) of the mass at any time t.
N is required to keep the spring stretched m beyond its natural length. The spring is stretched 1m beyond its natural length and then released with zero velocity. Find the position x(t) of the mass at any time t. Question
A spring with a mass of 
kg has damping constant 28 and spring constant 
. Find the damping constant that would produce critical damping.
A)
B)
9 
C)
D)
E)
kg has damping constant 28 and spring constant . Find the damping constant that would produce critical damping.A)
B)
9 C)
D)
E)
Question
Solve the differential equation using the method of variation of parameters. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use power series to solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A series circuit consists of a resistor 
, an inductor with 
, a capacitor with 
, and a generator producing a voltage of 
If the initial charge is 
and the initial current is 0, find the charge 
at time t.
A)
B)
C)
D)
E)
, an inductor with , a capacitor with , and a generator producing a voltage of If the initial charge is and the initial current is 0, find the charge at time t.A)
B)
C)
D)
E)
Question
Use power series to solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A spring has a mass of 
kg and its damping constant is 
. The spring starts from its equilibrium position with a velocity of 
m/s. Graph the position function for the spring constant 
.
A)
B)
C)
kg and its damping constant is . The spring starts from its equilibrium position with a velocity of m/s. Graph the position function for the spring constant .A)
B)
C)
Question
A spring with a mass of 2 kg has damping constant 14, and a force of 
N is required to keep the spring stretched 
m beyond its natural length. Find the mass that would produce critical damping.
N is required to keep the spring stretched m beyond its natural length. Find the mass that would produce critical damping. Question
The figure shows a pendulum with length L and the angle 
from the vertical to the pendulum. It can be shown that 
, as a function of time, satisfies the nonlinear differential equation 
where 
we can use the linear approximation 
A)
B)
C)
D)
E)
from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation A)
B)
C)
D)
E)
Question
A spring with a 
-kg mass has natural length 
m and is maintained stretched to a length of 
m by a force of 
N. If the spring is compressed to a length of 
m and then released with zero velocity, find the position 
of the mass at any time 
.
A)
B)
C)
D)
E)
-kg mass has natural length m and is maintained stretched to a length of m by a force of N. If the spring is compressed to a length of m and then released with zero velocity, find the position of the mass at any time .A)
B)
C)
D)
E)
Question
The solution of the initial-value problem 
is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.
A)
B)
C)
D)
E)
is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.A)
B)
C)
D)
E)
Question
A series circuit consists of a resistor 
an inductor with L = 
H, a capacitor with
C =
F, and a 
-V battery. If the initial charge and current are both 0, find the charge Q(t) at time t.
an inductor with L = H, a capacitor withC =
F, and a -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t. Question
A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.
A)
B)
C)
A)
B)
C)
Question
Use power series to solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use power series to solve the differential equation.. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation using the method of variation of parameters. 
Question
Solve the differential equation using the method of undetermined coefficients. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation using the method of undetermined coefficients. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation. 
Question
Solve the differential equation using the method of undetermined coefficients. 
Question
Solve the initial-value problem using the method of undetermined coefficients. 
Question
Solve the initial-value problem using the method of undetermined coefficients. 
Question
Solve the differential equation using the method of undetermined coefficients. 
Question
Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation using the method of undetermined coefficients. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation using the method of variation of parameters. 
Question
Solve the differential equation using the method of variation of parameters. 
Question
Solve the differential equation using the method of variation of parameters. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation using the method of variation of parameters. 
Question
Solve the differential equation using the method of variation of parameters. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation. 
Question
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Graph the particular solution and several other solutions. 
A)
B)
C)
A)
B)
C)
Question
Solve the differential equation using the method of variation of parameters. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the boundary-value problem, if possible. 
A)
B)
C)
D)
E)No solution
A)
B)
C)
D)
E)No solution
Question
Solve the initial-value problem. 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the initial-value problem. 
A)
B)
C)
D)
E)None of these
A)
B)
C)
D)
E)None of these
Question
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find f by solving the initial value problem. 
; 
, 
A)
+ 4 
x - 10
B)
+ 2 
x 
C)
+ 4 
x - 5
D)
+ 2 
x 
; , A)
+ 4 x - 10B)
+ 2 x C)
+ 4 x - 5D)
+ 2 x Question
Solve the differential equation. 
A)
B)
C)
D)
E)None of these
A)
B)
C)
D)
E)None of these
Question
Solve the initial-value problem. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation. 
Question
Solve the differential equation. 
Question
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the initial-value problem. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the differential equation. 
Question
Solve the initial-value problem. 
Question
Solve the initial-value problem. 
Question
Solve the initial value problem. 
Question
Solve the differential equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the boundary-value problem, if possible. 
A)
B)
C)
D)
E)No solution
A)
B)
C)
D)
E)No solution
Question
Solve the boundary-value problem, if possible. 
Question
Solve the differential equation. 
Question
Solve the boundary-value problem, if possible. 
Question
Solve the initial-value problem. 
Question
Solve the differential equation. 
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Deck 17: Second-Order Differential Equations
1
Suppose a spring has mass M and spring constant k and let . Suppose that the damping constant is so small that the damping force is negligible. If an external force is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.
A)
B)
C)
D)
E)
. Suppose that the damping constant is so small that the damping force is negligible. If an external force is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.A)
B)
C)
D)
E)
2
A series circuit consists of a resistor , an inductor with , a capacitor with , and a -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.
A)
B)
C)
D)
E)
, an inductor with , a capacitor with , and a -V battery. If the initial charge is 0.0008 C and the initial current is 0, find the current I(t) at time t.A)
B)
C)
D)
E)
3
A spring with a 3-kg mass is held stretched 0.9 m beyond its natural length by a force of 30 N. If the spring begins at its equilibrium position but a push gives it an initial velocity of m/s, find the position x(t) of the mass after t seconds.
A)
B)
C)
D)
E)
m/s, find the position x(t) of the mass after t seconds.A)
B)
C)
D)
E)
4
Use power series to solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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5
Use power series to solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
Unlock Deck
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6
A spring with a mass of 2 kg has damping constant 14, and a force of N is required to keep the spring stretched m beyond its natural length. The spring is stretched 1m beyond its natural length and then released with zero velocity. Find the position x(t) of the mass at any time t.
N is required to keep the spring stretched m beyond its natural length. The spring is stretched 1m beyond its natural length and then released with zero velocity. Find the position x(t) of the mass at any time t. Unlock Deck
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7
A spring with a mass of kg has damping constant 28 and spring constant . Find the damping constant that would produce critical damping.
A)
B) 9
C)
D)
E)
kg has damping constant 28 and spring constant . Find the damping constant that would produce critical damping.A)
B)
9 C)
D)
E)
Unlock Deck
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k this deck
8
Solve the differential equation using the method of variation of parameters.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
9
Use power series to solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
Unlock Deck
k this deck
10
A series circuit consists of a resistor , an inductor with , a capacitor with , and a generator producing a voltage of If the initial charge is and the initial current is 0, find the charge at time t.
A)
B)
C)
D)
E)
, an inductor with , a capacitor with , and a generator producing a voltage of If the initial charge is and the initial current is 0, find the charge at time t.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
11
Use power series to solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
Unlock Deck
k this deck
12
A spring has a mass of kg and its damping constant is . The spring starts from its equilibrium position with a velocity of m/s. Graph the position function for the spring constant .
A)
B)
C)
kg and its damping constant is . The spring starts from its equilibrium position with a velocity of m/s. Graph the position function for the spring constant .A)
B)
C)
Unlock Deck
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13
A spring with a mass of 2 kg has damping constant 14, and a force of N is required to keep the spring stretched m beyond its natural length. Find the mass that would produce critical damping.
N is required to keep the spring stretched m beyond its natural length. Find the mass that would produce critical damping. Unlock Deck
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k this deck
14
The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation
A)
B)
C)
D)
E)
from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where we can use the linear approximation A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
Unlock Deck
k this deck
15
A spring with a -kg mass has natural length m and is maintained stretched to a length of m by a force of N. If the spring is compressed to a length of m and then released with zero velocity, find the position of the mass at any time .
A)
B)
C)
D)
E)
-kg mass has natural length m and is maintained stretched to a length of m by a force of N. If the spring is compressed to a length of m and then released with zero velocity, find the position of the mass at any time .A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
Unlock Deck
k this deck
16
The solution of the initial-value problem is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.
A)
B)
C)
D)
E)
is called a Bessel function of order 0. Solve the initial - value problem to find a power series expansion for the Bessel function.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
Unlock Deck
k this deck
17
A series circuit consists of a resistor an inductor with L = H, a capacitor with
C = F, and a -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t.
an inductor with L = H, a capacitor withC =
F, and a -V battery. If the initial charge and current are both 0, find the charge Q(t) at time t. Unlock Deck
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k this deck
18
A spring with a mass of 2 kg has damping constant 8 and spring constant 80. Graph the position function of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s.
A)
B)
C)
A)
B)
C)
Unlock Deck
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k this deck
19
Use power series to solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
Unlock Deck
k this deck
20
Use power series to solve the differential equation..
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
21
Solve the differential equation using the method of variation of parameters.
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22
Solve the differential equation using the method of undetermined coefficients.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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23
Solve the differential equation using the method of undetermined coefficients.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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24
Solve the differential equation.
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25
Solve the differential equation using the method of undetermined coefficients.
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26
Solve the initial-value problem using the method of undetermined coefficients.
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27
Solve the initial-value problem using the method of undetermined coefficients.
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28
Solve the differential equation using the method of undetermined coefficients.
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k this deck
29
Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
30
Solve the differential equation using the method of undetermined coefficients.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
31
Solve the differential equation using the method of variation of parameters.
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k this deck
32
Solve the differential equation using the method of variation of parameters.
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k this deck
33
Solve the differential equation using the method of variation of parameters.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
Unlock Deck
k this deck
34
Solve the differential equation using the method of variation of parameters.
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Unlock Deck
k this deck
35
Solve the differential equation using the method of variation of parameters.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
Unlock Deck
k this deck
36
Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
37
Solve the differential equation.
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k this deck
38
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
39
Graph the particular solution and several other solutions.
A)
B)
C)
A)
B)
C)
Unlock Deck
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Unlock Deck
k this deck
40
Solve the differential equation using the method of variation of parameters.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
Unlock Deck
k this deck
41
Solve the boundary-value problem, if possible.
A)
B)
C)
D)
E)No solution
A)
B)
C)
D)
E)No solution
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42
Solve the initial-value problem. .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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Unlock Deck
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43
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
Unlock Deck
k this deck
44
Solve the initial-value problem.
A)
B)
C)
D)
E)None of these
A)
B)
C)
D)
E)None of these
Unlock Deck
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k this deck
45
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
46
Find f by solving the initial value problem. ; ,
A) + 4 x - 10
B) + 2 x
C) + 4 x - 5
D) + 2 x
; , A)
+ 4 x - 10B)
+ 2 x C)
+ 4 x - 5D)
+ 2 x Unlock Deck
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Unlock Deck
k this deck
47
Solve the differential equation.
A)
B)
C)
D)
E)None of these
A)
B)
C)
D)
E)None of these
Unlock Deck
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k this deck
48
Solve the initial-value problem.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
49
Solve the differential equation.
Unlock Deck
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50
Solve the differential equation.
Unlock Deck
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51
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
52
Solve the initial-value problem.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
53
Solve the differential equation.
Unlock Deck
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54
Solve the initial-value problem.
Unlock Deck
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55
Solve the initial-value problem.
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56
Solve the initial value problem.
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Unlock for access to all 63 flashcards in this deck.
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57
Solve the differential equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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58
Solve the boundary-value problem, if possible.
A)
B)
C)
D)
E)No solution
A)
B)
C)
D)
E)No solution
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k this deck
59
Solve the boundary-value problem, if possible.
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60
Solve the differential equation.
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61
Solve the boundary-value problem, if possible.
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k this deck
62
Solve the initial-value problem.
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Unlock for access to all 63 flashcards in this deck.
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63
Solve the differential equation.
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k this deck
Unlock Deck
Unlock for access to all 63 flashcards in this deck.
