Question 1

Find the recurrence relation for the general power series solution   to the second order equation   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 2

A 0.15 kg mass hangs on a spring with a 2 N m-1 force constant and its motion is damped proportional to its velocity with proportionality constant 0.4 kg s-1. If the system is subjected to an external variable-frequency vibration described as   newtons, what will be the amplitude of the steady-state oscillation?

Accepted Answer

A)  1.32 m 
B)  1.74 m 
C)  0.53 m 
D)  0.00 m 
A)  1.32 m 
B)  1.74 m 
C)  0.53 m 
D)  0.00 m

Question 3

Determine the form of a particular solution of the equation.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 4

Identify the general solution of the the differential equation   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

A second order differential equation can be arranged to the form   , and one can find the third and higher derivatives of y by simply differentiating this equation. Since a Taylor-series expansion of a function y(x) is   , one can differentiate the rearranged second order differential equation to evaluate coefficients in the Taylor polynomial, if one is either given or can solve for the initial condition y(0) and y'(0). What is the coefficient of x4 in the Taylor polynomial expansion of the solution to the equation   if the initial conditions are   ?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Identify the form of a particular solution to the equation   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 7

A certain spring is at rest when stretched 0.098 m by a 2.0 kg mass. Which function describes the motion of the mass if it is pulled down 0.25 m and released without imparting any initial velocity at time t = 0? Other helpful information: the motion is not damped; use 9.8 m s-2 as the acceleration due to gravity; and consider the zero position to be the rest position of the spring with the mass attached, and downward motion defines the positive x direction.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 8

Solve the initial value problem.

Accepted Answer

The answer of Solve the initial value problem.  ...

Question 9

A series circuit has a 0.25 henry inductor, a 340 ohm resistor, and a 0.000009 farad capacitor. There is an initial charge of 0.000004 coulombs, there is no initial current, and there is an applied voltage which is described as   . Identify the amplitude of the steady-state solution.

Accepted Answer

A)  0.000003 
B)  0.000009 
C)  0.35 
D)  0.175 
A)  0.000003 
B)  0.000009 
C)  0.35 
D)  0.175

Question 10

Solve the initial value problem   ,   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

Find the general solution of the equation   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

A spring is stretched 2 cm by a 1-kg mass. The mass is set in motion from its equilibrium position with an upward velocity of 4 m/s. The damping constant equals   Find an equation for the position of the mass at any time t.

Accepted Answer

The answer of A spring is stretched 2 cm by...

Question 13

A series circuit has a 0.15 henry inductor, a 490 ohm resistor, and a 0.000004 farad capacitor. There is an applied voltage which is described as   . Identify the general solution to the differential equation that describes the charge on the capacitor as a function of time.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

Identify the general solution of the the differential equation   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 15

Suppose that the charge in a circuit satisfies the equation   Find the gain of the circuit.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 16

Find the recurrence relation for the general power series solution   to the second order equation   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

A series circuit has an 0.3 henry inductor, a 300 ohm resistor, and a 10-3 farad capacitor. The initial charge on the capacitor is 10-7 coulombs, and there is no initial current nor applied voltage. Identify the function that describes the charge on the capacitor as a function of time.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 18

Identify the radius of convergence of the power series solutions about x = 0 of   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Find the recurrence relation for the general power series solution to the second order equation .

Determine the form of a particular solution of the equation.

Identify the general solution of the the differential equation .

Identify the form of a particular solution to the equation .

Solve the initial value problem.

A series circuit has a 0.25 henry inductor, a 340 ohm resistor, and a 0.000009 farad capacitor. There is an initial charge of 0.000004 coulombs, there is no initial current, and there is an applied voltage which is described as . Identify the amplitude of the steady-state solution.

Solve the initial value problem , .

Find the general solution of the equation .

A spring is stretched 2 cm by a 1-kg mass. The mass is set in motion from its equilibrium position with an upward velocity of 4 m/s. The damping constant equals Find an equation for the position of the mass at any time t.

A series circuit has a 0.15 henry inductor, a 490 ohm resistor, and a 0.000004 farad capacitor. There is an applied voltage which is described as . Identify the general solution to the differential equation that describes the charge on the capacitor as a function of time.

Identify the general solution of the the differential equation .

Suppose that the charge in a circuit satisfies the equation Find the gain of the circuit.

Find the recurrence relation for the general power series solution to the second order equation .

A series circuit has an 0.3 henry inductor, a 300 ohm resistor, and a 10^-3 farad capacitor. The initial charge on the capacitor is 10^-7coulombs, and there is no initial current nor applied voltage. Identify the function that describes the charge on the capacitor as a function of time.

Identify the radius of convergence of the power series solutions about x = 0 of .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Filters

Exam 17: Second Order Differential Equations

Find the recurrence relation for the general power series solution to the second order equation .

Determine the form of a particular solution of the equation.

Identify the general solution of the the differential equation .

Identify the form of a particular solution to the equation .

Solve the initial value problem.

A series circuit has a 0.25 henry inductor, a 340 ohm resistor, and a 0.000009 farad capacitor. There is an initial charge of 0.000004 coulombs, there is no initial current, and there is an applied voltage which is described as . Identify the amplitude of the steady-state solution.

Solve the initial value problem , .

Find the general solution of the equation .

A spring is stretched 2 cm by a 1-kg mass. The mass is set in motion from its equilibrium position with an upward velocity of 4 m/s. The damping constant equals Find an equation for the position of the mass at any time t.

A series circuit has a 0.15 henry inductor, a 490 ohm resistor, and a 0.000004 farad capacitor. There is an applied voltage which is described as . Identify the general solution to the differential equation that describes the charge on the capacitor as a function of time.

Identify the general solution of the the differential equation .

Suppose that the charge in a circuit satisfies the equation Find the gain of the circuit.

Find the recurrence relation for the general power series solution to the second order equation .

A series circuit has an 0.3 henry inductor, a 300 ohm resistor, and a 10-3 farad capacitor. The initial charge on the capacitor is 10-7 coulombs, and there is no initial current nor applied voltage. Identify the function that describes the charge on the capacitor as a function of time.

Identify the radius of convergence of the power series solutions about x = 0 of .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Filters

A series circuit has an 0.3 henry inductor, a 300 ohm resistor, and a 10^-3 farad capacitor. The initial charge on the capacitor is 10^-7coulombs, and there is no initial current nor applied voltage. Identify the function that describes the charge on the capacitor as a function of time.