Exercise Solution
1. A mass on a spring undergoes simple harmonic motion (SHM).
When the mass is at its maximum displacement from equilibrium, its
instantaneous velocity
A) is maximum.
B) is less than maximum, but not zero.
C) is zero.
D) cannot be determined from the information given.
2. A mass on a spring undergoes
SHM. When the mass is at maximum
displacement from equilibrium, its instantaneous acceleration
A) is a maximum.
B) is less than maximum, but not zero.
C) is zero.
D) cannot be determined from the information given
3. 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 kinetic energy is a minimum?
A) at either A or B
B) midway between A and B
C) one-fourth of the way between A and B
D) none of the above
4. Doubling only the amplitude
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) increases the energy by a factor of three
C) increases the energy by a factor of four
D) produces no change
5. A mass oscillates on the end
of a spring, both on Earth and on the Moon.
Where is the period the greatest?
A) Earth
B) the Moon
C) same on both Earth and the Moon
D) cannot be determined from the information given
6. 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 proportional to the amplitude.
B) the period is proportional to the amplitude.
C) the frequency is independent of the mass M.
D) the frequency is independent of the length L.
7. When the length of a simple
pendulum is tripled, the time for one complete vibration increases by a
factor of
A) 3.
B) 2.
C) 1.7.
D) 1.4.
8. What happens to a simple
pendulum's frequency if both its length and mass are increased?
A) It increases.
B) It decreases.
C) It remains constant.
D) It could remain constant, increase, or decrease; it depends on the length
to mass ratio.
9. For a forced vibration, the
amplitude of vibration is found to depend on the
A) sum of the external frequency and the natural frequency.
B) difference of the external frequency and the natural frequency.
C) product of the external frequency and the natural frequency.
D) ratio of the external frequency and the natural frequency.
10. The number of crests of a
wave passing a point per unit time is called the wave's
A) speed.
B) frequency.
C) wavelength.
D) amplitude.
11. A wave moves on a string with wavelength λ and frequency f. A second wave on the same string has wavelength 2λ and travels with the same velocity.
What is the frequency of the second wave?
A) 0.5f
B) f
C) 2f
D) It cannot be determined from the information given.
12. Consider a traveling wave
on a string of length L, mass M, and tension T.
A standing wave is set up. Which of the following is true?
A) The wave velocity depends on M, L, T.
B) The wavelength of the wave is proportional to the frequency.
C) The particle velocity is equal to the wave velocity.
D) The wavelength is proportional to T.
13. A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and
transmitted pulses?
A) Both are right side up.
B) The reflected pulse returns right side up while the transmitted pulse is
inverted.
C) The reflected pulse returns inverted while the transmitted pulse is right
side up.
D) Both are inverted.
14. Resonance in a system, such
as a string fixed at both ends, occurs when
A) it is oscillating in simple harmonic motion.
B) its frequency is the same as the frequency of an external source.
C) its frequency is greater than the frequency of an external source.
D) its frequency is smaller than the frequency of an external source.
15. If one doubles the tension
in a violin string, the fundamental frequency of that string will increase
by a factor of
A) 2.
B) 4.
C) 1.4.
D) 1.7.
16. What is the spring constant
of a spring that stretches 2.00 cm when a mass of 0.600 kg is suspended from
it?
A) 0.300 N/m
B) 30.0 N/m
C) 2.94 N/m
D) 294 N/m
17. A mass vibrates back and forth from the free end of an ideal spring of spring constant 20 N/m with an amplitude of 0.30 m. What is the kinetic energy of this vibrating
mass when it is 0.30 m from its equilibrium position?
A) zero
B) 0.90 J
C) 0.45 J
D) It is impossible to give an answer without knowing the object's mass.
18. A mass undergoes SHM with
amplitude of 4 cm. The energy is
8.0 J at this time. The mass is
cut in half, and the system is again set in motion with amplitude 4.0 cm.
What is the energy of the system now?
A) 2.0 J
B) 4.0 J
C) 8.0 J
D) 16 J
19. A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a
speed of 1.5 m/s at the equilibrium position.
What is the amplitude of vibration?
A) 0.024 m
B) 0.058 m
C) 0.24 m
20. The mass of a mass-and-spring system is displaced 10 cm from its equilibrium position and released. A frequency of 4.0 Hz is observed. What frequency would be
observed
if the mass had been displaced only 5.0 cm and then released?
A) 2.0 Hz
B) 4.0 Hz
C) 8.0 Hz
D) none of the above
21. An object in simple
harmonic motion obeys the following position versus time equation: y = (0.50
m) sin (π/2 t). What is the
amplitude of vibration?
A) 0.25 m
B) 0.50 m
C) 0.75 m
D) 1.0 m
22. A pendulum has a period of
2.0 s on Earth. What is its length?
A) 2.0 m
B) 1.0 m
C) 0.70 m
D) 0.50 m
23. A string of linear density
6.0 g/m is under a tension of 180 N. What is the velocity of
propagation of transverse waves along the string?
A) 2.9 x 104 m/s
B) 1.7 x 102 m/s
C) 13 m/s
D) 5.8 x 10-3 m/s
24. A string, fixed at both ends, vibrates at a frequency of 12 Hz with a standing transverse wave pattern containing 3 loops. What frequency is needed if the standing wave
pattern is to contain 4 loops?
A) 48 Hz
B) 36 Hz
C) 16 Hz
D) 12 Hz