SHM Concepts 2

Grandfather clocks are designed in a way that the weight at the bottom of the pendulum can be moved up or down by turning a small screw. Suppose you have a grandfather clock at home that runs fast. Should you turn the adjusting screw so as to raise the weight or lower the weight? a. Lower it. b. It doesn't matter if you raise or lower the weight, as long as you displace it by the right amount. c. Raise it. d. It doesn't matter if you raise or lower the weight, as long as you displace it with the correct initial velocity. e. Raising or lowering the weight doesn't help, the screw is there so that you can add or take away weight.

a. Lower it.

Which of the following are characteristics of a mass in simple harmonic motion? I. The motion repeats at regular intervals. II. The motion is sinusoidal. III. The restoring force is proportional to the displacement from equilibrium. a. all of the above b. II and III only c. I and II only d. I and III only e. none of the above

a. all of the above

Doubling only the amplitude of a vibrating mass-and-spring system produces what effect on the system's mechanical energy? a. produces no change b. increases the energy by a factor of two c. increases the energy by a factor of three d. increases the energy by a factor of four

a. produces no change ME = KE + PE = (1/2)(mv^2) + (1/2)(kx^2) Since the mechanical energy does not depend on amplitude, a change in the amplitude has no effect on the mechanical energy.

Both pendulum A and B are 3.0 m long. The period of A is T. Pendulum A is twice as heavy as pendulum B. What is the period of B? a. 1.4T b. 0.71T c. 2T d. T e. 3T

b. 0.71T T (period of A) = 2(pi)(sqrt(m/k)) Period of B = 2(pi)(sqrt(m/2k)) = T/sqrt(2) = 0.71T

By what factor should the length of a simple pendulum be changed in order to triple the period of vibration? a. 6 b. 9 c. 3 d. 27

b. 9 T = 2(pi)(sqrt(L/g)) 3T = 2(pi)(sqrt(9L/g))

The graph below is a plot of displacement versus time of a mass oscillating on a spring https://ahsphysics.edumoot.com/pluginfile.php/374/question/questiontext/108554/28/5046/ppg__examview__SHM_Concepts_2__nar002-1.jpg At which point on the graph is the velocity of the mass zero? a. B b. A c. D d. C

b. A At this point, the mass momentarily stops, so its instantaneous velocity is zero.

A mass M is attached to a spring with spring constant k. 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. 4T b. T c. sqrt(2)*T d. T/2 e. 2T

b. T T = 2(pi)/w, and is therefore unaffected by changes in amplitude.

What happens when a periodic driving force is applied at a frequency close to the natural frequency of the system? a. The system will exhibit chaotic motion. b. The system will resonate and unless some energy is lost the amplitude of the vibrations will increase until the system breaks. c. The system will continue to vibrate in SHM as if nothing had happened. d. The system will stop vibrating and finally come to a stop. e. It will vibrate at some multiple of the driving frequency (call a harmonic or "overtone").

b. The system will resonate and unless some energy is lost the amplitude of the vibrations will increase until the system breaks.

On the Moon, the acceleration of gravity is g/6. If a pendulum has a period T on Earth, what will its period be on the Moon? a. 6T b. Tsqrt(6) c. T/3 d. T/sqrt(6) e. T/6

b. Tsqrt(6) T on Earth = 2(pi)sqrt(L/g) T on the moon = 2(pi)sqrt(L/(g/6)) = 2(pi)sqrt(6L/g) = sqrt(6) * (2(pi)*sqrt(L/g)) = T(sqrt(6))

Which of the following is not an example of approximate simple harmonic motion? a. a car's radio antenna waving back and forth b. a ball bouncing on the floor c. a child swinging on a swing d. a piano wire that has been struck

b. a ball bouncing on the floor

A mass attached to a spring vibrates back and forth. At maximum displacement, the spring force and the a. velocity reach a maximum. b. acceleration reach a maximum. c. velocity reach zero. d. acceleration reach zero.

b. acceleration reach a maximum.

Curve C in Fig. 11-1 represents a. an underdamped situation. b. an overdamped situation. c. critical damping. d. a moderately damped situation.

b. an overdamped situation.

A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its total energy is a minimum? a. one-fourth of the way between A and B b. none of the above c. at either A or B d. midway between A and B

b. none of the above The total energy remains constant.

Doubling only the mass of a vibrating mass-and-spring system produces what effect on the system's mechanical energy? a. increases the energy by a factor of two b. produces no change c. increases the energy by a factor of three d. increases the energy by a factor of four

b. produces no change

The velocity of a mass attached to a spring is given by v = (1.5 cm/s) sin(ùt + ð/2), where ù = 3.0 rad/s. What is the corresponding expression for x? a. x = -(4.50 cm) sin(ùt + ð/2) b. x = -(0.50 cm) sin(ùt + ð/2) c. x = -(0.50 cm) cos(ùt - ð/2) d. x = (4.50 cm) cos(ùt + ð/2) e. x = -(0.50 cm) cos(ùt + ð/2)

b. x = -(0.50 cm) sin(ùt + ð/2) v = Awsin(ùt + ð) => Aw = 3A = 1.5 => A = 0.5 cm x = Acos(ùt + ð) = -(0.5) cos(ùt + ð)

Tripling the displacement from equilibrium of an object in simple harmonic motion will change the magnitude of the object's maximum acceleration by what factor? a. 9 b. one-third c. 3 d. 1

c. 3 Initial Amax = Aw^2 Final Amax = 3Aw^2 Therefore, tripling the displacement from equilibrium will cause Amax to increase by a factor of 3/1 = 3.

The graph below is a plot of displacement versus time of a mass oscillating on a spring. At which point on the graph is the acceleration of the mass zero? a. A b. B c. C d. D https://ahsphysics.edumoot.com/pluginfile.php/374/question/questiontext/108554/26/5040/ppg__examview__SHM_Concepts_2__nar002-1.jpg

c. C The displacement at C is zero. Since the acceleration is proportional to displacement, the acceleration is also zero at C.

A mass m is suspended from the ceiling of an elevator by a spring of force constant k. When the elevator is at rest, the period of the mass is T. How does the period of the mass change when the elevator moves upward with constant acceleration? a. It becomes zero. b. It increases. c. It does not change. d. It decreases. e. It depends on how much you stretch the spring.

c. It does not change.

For a mass hanging from a spring, the maximum displacement the spring is stretched or compressed from its equilibrium position is the system's a. period. b. acceleration. c. amplitude. d. frequency.

c. amplitude.

Curve B in Fig. 11-1 represents a. a moderately damped situation. b. an overdamped situation. c. critical damping. d. an underdamped situation.

c. critical damping.

A simple pendulum swings in simple harmonic motion. At maximum displacement, a. the restoring force reaches zero. b. the acceleration reaches zero. c. the acceleration reaches a maximum. d. the velocity reaches a maximum.

c. the acceleration reaches a maximum.

A simple pendulum consists of a mass M attached to a weightless string of length L. For this system, when undergoing small oscillations a. the frequency is inversely proportional to the amplitude. b. the frequency is independent of the length L. c. the frequency is independent of the mass M. d. the frequency is proportional to the amplitude. e. the period is proportional to the amplitude.

c. the frequency is independent of the mass M.

A mass is attached to a vertical spring and bobs up and down between points A and B. As time passes the maximum amplitude of the oscillations is seen to smaller until finally the oscillations stop. This happens because a. the potential energy of the mass-spring system is decreasing b. none of the above c. the total energy of the mass-spring system is decreasing d. the kinetic energy of the mass-spring system is decreasing

c. the total energy of the mass-spring system is decreasing

A mass attached to a spring vibrates back and forth. At the equilibrium position, the a. net force reaches a maximum. b. acceleration reaches a maximum. c. velocity reaches a maximum. d. velocity reaches zero.

c. velocity reaches a maximum.

If the amplitude of the motion of a simple harmonic oscillator is doubled, by what factor does the frequency of the oscillator change? a. 1/4 b. 4 c. 2 d. 1 e. 1/2

d. 1 The formula for f is 2(pi)/w. It doesn't depend on the amplitude.

The graph below is a plot of displacement versus time of a mass oscillating on a spring. https://ahsphysics.edumoot.com/pluginfile.php/374/question/questiontext/108554/27/5043/ppg__examview__SHM_Concepts_2__nar002-1.jpg At which point on the graph is the net force on the mass at a maximum? a. C b. D c. B d. A

d. A

A simple harmonic oscillator is undergoing oscillations with an amplitude A. How far is it from its equilibrium position when the kinetic and potential energies are equal? a. A b. A/sqrt(3) c. A/3 d. A/sqrt(2) e. A/2

d. A/sqrt(2)

A mass is attached to a vertical spring and bobs up and down between points A and B. As time passes the maximum amplitude of the oscillations is seen to smaller until finally the oscillations stop. What happens to the time period and the angular frequency of the mass's oscillations as the amplitude declines a. The time period increases and the angular frequency increases. b. The time period decreases and the angular frequency increases. c. The time period decreases and the angular frequency decreases. d. The time period remains constant and the angular frequency remains constant e. The time period increases and the angular frequency decreases.

d. The time period remains constant and the angular frequency remains constant

Which of following is a graph of simple periodic motion with amplitude 2.00 cm, angular frequency 2.00 s-1?

???

Curve A in Fig. 11-1 represents a. a moderately damped situation. b. an overdamped situation. c. critical damping. d. an underdamped situation. https://ahsphysics.edumoot.com/pluginfile.php/374/question/questiontext/108554/16/4974/ppg__examview__SHM_Concepts_2__nar001-1.jpg

d. an underdamped situation.

The total mechanical energy of a simple harmonic oscillator is a. zero when it reaches the maximum displacement. b. a minimum when it passes through the equilibrium point. c. zero as it passes the equilibrium point. d. constant. e. a maximum when it passes through the equilibrium point.

d. constant. When the kinetic energy decreases, the potential increases and vice versa. Since the mechanical energy is the sum of the kinetic and potential energy, the total mechanical energy always remains constant.

Vibration of an object about an equilibrium point is called simple harmonic motion when the restoring force is proportional to a. mass. b. time. c. a spring constant. d. displacement.

d. displacement. F = -kx, where x is the displacement.

In simple harmonic motion, the acceleration is proportional to a. all of the above b. the amplitude. c. the velocity. d. the displacement. e. the frequency.

d. the displacement.

Doubling only the spring constant of a vibrating mass-and-spring system produces what effect on the system's mechanical energy? a. increases the energy by a factor of four b. produces no change c. increases the energy by a factor of three d. increases the energy by a factor of two

Initial ME = KE + PE = (1/2)mv^2 + (1/2)kx^2 = (1/2)(mv^2 + kx^2) Final ME = KE + PE = (1/2)mv^2 + (1/2)(2k)x^2 = (1/2)mv^2 + kx^2

The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26 s-1)t]. What is the velocity of the mass when t = 0.815 s? a. - 13.3 cm/s b. 8.02 cm/s c. 0 cm/s d. - 8.02 cm/s e. 13.3 cm/s

a. - 13.3 cm/s x = A cos(wt) => A = 12.3 cm, w = 1.26 s-1 v = -Aw sin(wt) = -(12.3) * (1.26) * sin(1.26 * 0.815) = - 13.3 cm/s

If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum acceleration of the oscillator change? a. 4 b. 1/4 c. 1 d. 2 e. 1/2

a. 4 Initial amax = Aw^2 = A[2(pi)f]^2 = 4A(pi)^2*f^2 Final amax = Aw^2 = A[2(pi)2f]^2 = 16A(pi)^2*f^2 amax increases by a factor of 16/4 = 4.

The work done to move a spring away from its equilibrium position is equal to a. the kinetic energy of the spring. b. the ratio of force to displacement. c. the ratio of force to mass. d. the potential energy of the spring.

d. the potential energy of the spring.

If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change? a. 1/4 b. 1/2 c. 4 d. 1 e. 2

e. 2 Initial Vmax = Aw = A[2(pi)*f] = 2A(pi)f Final Vmax = Aw = A[2(pi)*2f] = 4A(pi)f The maximum speed changes by a factor of 4/2 = 2.