1. If a mass on a spring and a pendulum have the same period on the moon where the
gravity is about 1/6 of its value on the Earth, which one will run faster on the Earth?
a. The mass on the spring.
b. The pendulum.
c. They will both run the same.
d. It depends on which one has the larger mass.
2. Which of the following quantities is at a maximum when an object in simple harmonic
motion is at its maximum displacement?
a. Velocity
b. Acceleration.
c. Kinetic energy
d. None of the above
3. Suppose there is an object which is subject to a force which follows the relation F = +kx.
What will happen to the object if it is moved away from the equilibrium position (x = 0)
and released?
a. It will remain stationary.
b. It will return to the equilibrium position.
c. It will move farther away with constant velocity.
d. It will move farther away with constant acceleration.
e. It will move farther away with increasing acceleration.
4. The amplitude of an object experiencing simple harmonic motion is doubled. Which of
the following is also doubled?
a. Maximum velocity
b. Total energy
c. Frequency
d. Period
e. Everything associated with the motion will be doubled.
5. A pendulum is made of a very long string with a hollow ball filled with water attached to
the end. The ball and the water have equal masses. There is a small hole in the ball and
water slowly leaks out. What happens to the frequency of the pendulum as the water
leaks?
a. It will double.
b. It will be cut in half.
c. It will increase by a factor of 2 .
d. It will decrease by a factor of 2 .
e. It will stay constant.
6. The kinetic energy and potential energy of an oscillator in simple harmonic motion are
equal to each other when the magnitude of the displacement from the equilibrium
position is what fraction of the total amplitude?
a. 1
b. 1/2
c. 1/3
d. 1/ 2
e. 1/ 3
Problems 7–9 are related to the following scenario:
7. If all the oscillators were driven by a device with a frequency of 4.6 Hz, which of the
oscillators would respond most strongly?
a. A
b. B
c. C
d. D
e. E
8. If one of the oscillators is critically damped, which one is it?
a. A
b. B
c. C
d. D
e. E
We have a collection of 5 different mass/spring combinations that all have different
properties. All of them have some damping and all have the same mass. The properties are
summarized in the table below:
Name Natural Frequency
(cycles/second)
Time for oscillation
to stop
(seconds)
Notes
A 2.0 100 sec.
B 5.0 300 sec.
C 20.0 100 sec.
D — 10 sec. Does not oscillate.
E — 50 sec. Does not oscillate. The
mass and spring are the
same as in D.
9. Which of the oscillators has the weakest damping coefficient?
a. A
b. B
c. C
d. D
e. E
My answers are as follows, just looking for a check
1 d
2 a
3 c
4 a
5 e
6 a
7 c
8 a
9 e
Here are the explanations for each question and the correct answers:
1. To determine which one will run faster on Earth, we need to understand the relationship between period and gravity. The period of a mass-spring system is given by T = 2π√(m/k), where m is the mass and k is the spring constant. The period of a pendulum is given by T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. Since the period on the moon is the same for both systems, we can set up the equation (2π√(m/k)) / 6 = (2π√(L/g)), and solve for m and L. But since the question asks about the behavior on Earth, the correct answer is (d) It depends on which one has the larger mass.
2. When an object in simple harmonic motion is at its maximum displacement, its velocity is zero, since it momentarily comes to rest before changing direction. Acceleration, on the other hand, is maximum at maximum displacement, as it is responsible for changing the object's direction. Therefore, the correct answer is (b) Acceleration.
3. The force F = -kx represents a restoring force that tries to bring the object back to the equilibrium position, where x = 0. If the object is moved away from the equilibrium position and released, it will experience a force that pulls it back towards the equilibrium position, resulting in oscillatory motion. Therefore, the correct answer is (b) It will return to the equilibrium position.
4. The amplitude of an object undergoing simple harmonic motion does not affect the frequency or period of the motion. Therefore, the correct answer is (e) Everything associated with the motion will be doubled.
5. The frequency of a pendulum is determined by the length of the string and the acceleration due to gravity. As the water leaks out of the hollow ball attached to the pendulum, the mass of the ball decreases, which does not affect the length of the string or the acceleration due to gravity. Therefore, the frequency stays constant. The correct answer is (e) It will stay constant.
6. The kinetic energy and potential energy of an oscillator in simple harmonic motion are equal when the object is at its maximum displacement (amplitude). Therefore, the correct answer is (a) 1.
7. To determine which oscillator would respond most strongly to the device with a frequency of 4.6 Hz, we look for the oscillator with a natural frequency closest to 4.6 Hz. The closest natural frequency is 5.0 Hz, so the correct answer is (b) B.
8. If an oscillator is critically damped, it means it is damped just enough to prevent oscillations from occurring. In this scenario, oscillator A has a damping coefficient that causes it to stop oscillating in 100 seconds, which is the shortest time for oscillation to stop. Therefore, the correct answer is (a) A.
9. The damping coefficient represents the rate at which the oscillations of an oscillator are reduced. In this scenario, oscillator E has the longest time for oscillation to stop (50 seconds) compared to the others, indicating the weakest damping coefficient. Therefore, the correct answer is (e) E.
Your answers are mostly correct except for question 1. The correct answer is (c) They will both run the same on Earth.