Question 1

Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s?

Accepted Answer

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

Question 2

A 0.25 kg ideal harmonic oscillator has a total mechanical energy of 4.0 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency?

Accepted Answer

A)  4.5 Hz 
B)  1.4 Hz 
C)  2.3 Hz 
D)  3.2 Hz 
A)  4.5 Hz 
B)  1.4 Hz 
C)  2.3 Hz 
D)  3.2 Hz

Question 3

In simple harmonic motion, the speed is greatest at that point in the cycle when

Accepted Answer

A)  the magnitude of the acceleration is a maximum. 
B)  the displacement is a maximum. 
C)  the magnitude of the acceleration is a minimum. 
D)  the potential energy is a maximum. 
E)  the kinetic energy is a minimum. 
A)  the magnitude of the acceleration is a maximum. 
B)  the displacement is a maximum. 
C)  the magnitude of the acceleration is a minimum. 
D)  the potential energy is a maximum. 
E)  the kinetic energy is a minimum.

Question 4

In the figure, a 0.24-kg ball is suspended from a very light string 9.79 m long and is pulled slightly to the left. As the ball swings without friction through the lowest part of its motion it encounters an ideal massless spring attached to the wall. The spring pushes against the ball and eventually the ball is returned to its original starting position. Find the time for one complete cycle of this motion if the spring constant of the spring is 21 N/m. (Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.)

Accepted Answer

The answer of In the figure, a 0.24-kg ball is...

Question 5

A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k1 and k2 whose opposite ends are fixed to walls, as shown in the figure. What is angular frequency of the oscillation if k1 = 7.6 N/m and k2 = 5.0 N/m?

Accepted Answer

A)  2.5 rad/s 
B)  3.5 rad/s 
C)  0.40 rad/s 
D)  0.56 rad/s 
A)  2.5 rad/s 
B)  3.5 rad/s 
C)  0.40 rad/s 
D)  0.56 rad/s

Question 6

A lightly damped harmonic oscillator, with a damping force proportional to its speed, is oscillating with an amplitude of 0.500 cm at time t = 0. When t = 8.20 s, the amplitude has died down to 0.400 cm. At what value of t will the oscillations have an amplitude of 0.250 cm?

Accepted Answer

A)  18.5 s 
B)  20.5 s 
C)  16.5 s 
D)  25.5 s 
E)  5.13 s 
A)  18.5 s 
B)  20.5 s 
C)  16.5 s 
D)  25.5 s 
E)  5.13 s

Question 7

A certain frictionless simple pendulum having a length L and mass M swings with period T. If both L and M are doubled, what is the new period?

Accepted Answer

A)  4T 
B)  2T 
C)    T 
D)  T 
E)  T/4 
A)  4T 
B)  2T 
C)    T 
D)  T 
E)  T/4

Question 8

A uniform meter stick is freely pivoted about the 0.20-m mark. If it is allowed to swing in a vertical plane with a small amplitude and friction, what is the frequency of its oscillations?

Accepted Answer

A)  0.55 Hz 
B)  0.66 Hz 
C)  0.92 Hz 
D)  1.1 Hz 
E)  1.3 Hz 
A)  0.55 Hz 
B)  0.66 Hz 
C)  0.92 Hz 
D)  1.1 Hz 
E)  1.3 Hz

Question 9

An object that weighs 2.450 N is attached to an ideal massless spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the spring constant of the spring?

Accepted Answer

A)  2.45 N/m 
B)  12.1 N/m 
C)  24.1 N/m 
D)  0.102 N/m 
E)  0.610 N/m 
A)  2.45 N/m 
B)  12.1 N/m 
C)  24.1 N/m 
D)  0.102 N/m 
E)  0.610 N/m

Question 10

A 2.00-kg object is attached to an ideal massless horizontal spring of spring constant 100.0 N/m and is at rest on a frictionless horizontal table. The spring is aligned along the x-axis and is fixed to a peg in the table. Suddenly this mass is struck by another 2.00-kg object traveling along the x-axis at 3.00 m/s, and the two masses stick together. What are the amplitude and period of the oscillations that result from this collision?

Accepted Answer

A)  0.300 m, 1.26 s 
B)  0.300 m, 0.889 s 
C)  0.424 m, 0.889 s 
D)  0.424 m, 1.26 s 
E)  0.424 m, 5.00 s 
A)  0.300 m, 1.26 s 
B)  0.300 m, 0.889 s 
C)  0.424 m, 0.889 s 
D)  0.424 m, 1.26 s 
E)  0.424 m, 5.00 s

Question 11

The position x of an object varies with time t. For which of the following equations relating x and t is the motion of the object simple harmonic motion? (There may be more than one correct choice.)

Accepted Answer

A)  x = 5 sin23t 
B)  x = 8 cos 3t 
C)  x = 4 tan 2t 
D)  x = 5 sin 3t 
E)  x = 2 cos(3t - 1) 
A)  x = 5 sin23t 
B)  x = 8 cos 3t 
C)  x = 4 tan 2t 
D)  x = 5 sin 3t 
E)  x = 2 cos(3t - 1)

Question 12

A 2.25-kg object is attached to a horizontal an ideal massless spring on a frictionless table. What should be the spring constant of this spring so that the maximum acceleration of the object will be g when it oscillates with amplitude of 4.50 cm?

Accepted Answer

The answer of A 2.25-kg object is attached to a...

Question 13

The position of an object that is oscillating on an ideal spring is given by the equation x = (12.3 cm) cos[(1.26s-1)t]. At time t = 0.815 s,
(a) how fast is the object moving?
(b) what is the magnitude of the acceleration of the object?

Accepted Answer

(a) 13.3 c

Question 14

An object weighing 44.1 N hangs from a vertical massless ideal spring. When set in vertical motion, the object obeys the equation y(t) = (6.20 cm) cos[(2.74 rad/s)t - 1.40].
(a) Find the time for this object to vibrate one complete cycle.
(b) What are the maximum speed and maximum acceleration of the object.
(c) What is the TOTAL distance the object moves through in one cycle.
(d) Find the maximum kinetic energy of the object.
(e) What is the spring constant of the spring.

Accepted Answer

(a) 2.29 s 
(b) 0.17

Question 15

A 25 kg object is undergoing lightly damped harmonic oscillations. If the maximum displacement of the object from its equilibrium point drops to 1/3 its original value in 1.8 s, what is the value of the damping constant b?

Accepted Answer

A)  31 kg/s 
B)  34 kg/s 
C)  37 kg/s 
D)  40 kg/s 
A)  31 kg/s 
B)  34 kg/s 
C)  37 kg/s 
D)  40 kg/s

Question 16

If we double only the spring constant of a vibrating ideal mass-and-spring system, the mechanical energy of the system

Accepted Answer

A)  increases by a factor of   . 
B)  increases by a factor of 2. 
C)  increases by a factor of 3. 
D)  increases by a factor of 4. 
E)  does not change. 
A)  increases by a factor of   . 
B)  increases by a factor of 2. 
C)  increases by a factor of 3. 
D)  increases by a factor of 4. 
E)  does not change.

Question 17

A mass M is attached to an ideal massless spring. When this system is set in motion with amplitude A, it has a period T. What is the period if the amplitude of the motion is increased to 2A?

Accepted Answer

A)  2T 
B)  T/2 
C)    T 
D)  4T 
E)  T 
A)  2T 
B)  T/2 
C)    T 
D)  4T 
E)  T

Question 18

A 1.5-kg mass attached to an ideal massless spring with a spring constant of 20.0 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the mass is released from rest at x = 10.0 cm. (That is, the spring is stretched by 10.0 cm.)
(a) Find the frequency of the oscillations.
(b) Determine the maximum speed of the mass. At what point in the motion does the maximum speed occur?
(c) What is the maximum acceleration of the mass? At what point in the motion does the maximum acceleration occur?
(d) Determine the total energy of the oscillating system.
(e) Express the displacement x as a function of time t.

Accepted Answer

(a) 0.58 Hz 
(b) 0.37 m/s, at

Question 19

A restoring force of magnitude F acts on a system with a displacement of magnitude x. In which of the following cases will the system undergo simple harmonic motion?

Accepted Answer

A)  F     
B)  F   sin x 
C)  F   x2 
D)  F   x 
E)  F   1/x 
A)  F     
B)  F   sin x 
C)  F   x2 
D)  F   x 
E)  F   1/x

Question 20

If we double only the mass of a vibrating ideal mass-and-spring system, the mechanical energy of the system

Accepted Answer

A)  increases by a factor of   . 
B)  increases by a factor of 2. 
C)  increases by a factor of 3. 
D)  increases by a factor of 4. 
E)  does not change. 
A)  increases by a factor of   . 
B)  increases by a factor of 2. 
C)  increases by a factor of 3. 
D)  increases by a factor of 4. 
E)  does not change.

Exam 14: Oscillations

Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s?

A 0.25 kg ideal harmonic oscillator has a total mechanical energy of 4.0 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency?

In simple harmonic motion, the speed is greatest at that point in the cycle when

A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k1 and k2 whose opposite ends are fixed to walls, as shown in the figure. What is angular frequency of the oscillation if k1 = 7.6 N/m and k2 = 5.0 N/m?

A lightly damped harmonic oscillator, with a damping force proportional to its speed, is oscillating with an amplitude of 0.500 cm at time t = 0. When t = 8.20 s, the amplitude has died down to 0.400 cm. At what value of t will the oscillations have an amplitude of 0.250 cm?

A certain frictionless simple pendulum having a length L and mass M swings with period T. If both L and M are doubled, what is the new period?

A uniform meter stick is freely pivoted about the 0.20-m mark. If it is allowed to swing in a vertical plane with a small amplitude and friction, what is the frequency of its oscillations?

An object that weighs 2.450 N is attached to an ideal massless spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the spring constant of the spring?

The position x of an object varies with time t. For which of the following equations relating x and t is the motion of the object simple harmonic motion? (There may be more than one correct choice.)

A 2.25-kg object is attached to a horizontal an ideal massless spring on a frictionless table. What should be the spring constant of this spring so that the maximum acceleration of the object will be g when it oscillates with amplitude of 4.50 cm?

The position of an object that is oscillating on an ideal spring is given by the equation x = (12.3 cm) cos[(1.26s-1)t]. At time t = 0.815 s, (a) how fast is the object moving? (b) what is the magnitude of the acceleration of the object?

A 25 kg object is undergoing lightly damped harmonic oscillations. If the maximum displacement of the object from its equilibrium point drops to 1/3 its original value in 1.8 s, what is the value of the damping constant b?

If we double only the spring constant of a vibrating ideal mass-and-spring system, the mechanical energy of the system

A mass M is attached to an ideal massless spring. When this system is set in motion with amplitude A, it has a period T. What is the period if the amplitude of the motion is increased to 2A?

A restoring force of magnitude F acts on a system with a displacement of magnitude x. In which of the following cases will the system undergo simple harmonic motion?

If we double only the mass of a vibrating ideal mass-and-spring system, the mechanical energy of the system

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A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k₁ and k₂ whose opposite ends are fixed to walls, as shown in the figure. What is angular frequency of the oscillation if k₁ = 7.6 N/m and k₂ = 5.0 N/m?

The position of an object that is oscillating on an ideal spring is given by the equation x = (12.3 cm) cos[(1.26s^-1)t]. At time t = 0.815 s, (a) how fast is the object moving? (b) what is the magnitude of the acceleration of the object?