For each of the following scenarios, indicate whether the oscillation period of the pendulum becomes shorter, longer or remains unchanged. Note: you must clearly mark your answer (for example, highlight it in red) from the multiple-choice list below and you must provide an explanation of your answer to receive credit. Review: course textbook (section 9.1).
a. The pendulum is transported to another planet where the acceleration due to gravity is smaller.
i. Shorter
ii. Longer
iii. Unchanged
Explanation:
b. The mass of the pendulum increases.
i. Shorter
ii. Longer
iii. Unchanged
Explanation:
c. The length of the pendulum decreases (i.e., the pendulum arm is shortened).
i. Shorter
ii. Longer
iii. Unchanged
Explanation:
d. The distance the pendulum travels or how far it travels from side to side (i.e., the amplitude of oscillation) is reduced.
i. Shorter
ii. Longer
iii. Unchanged
Explanation:
2. Consider a block attached to a spring shown in Figure 9.1.5 of the textbook.
For each of the following scenarios, indicate whether the oscillation period of the block becomes shorter, longer or remains unchanged. Note: you must clearly mark your answer (for example, highlight it in red) from the multiple-choice list below and you must provide an explanation of your answer to receive credit. Review: course textbook (section 9.1).
a. The mass of the block is reduced.
i. Shorter
ii. Longer
iii. Unchanged
Explanation:
b. The spring – mass device is transported to the Moon, where the acceleration due to gravity is weaker.
i. Shorter
ii. Longer
iii. Unchanged
Explanation:
c. The stiffness of the spring is reduced (i.e., the spring constant is lowered).
i. Shorter
ii. Longer
iii. Unchanged
Explanation:
d. The amplitude of the oscillation is increased (i.e., the distance the mass travels up and down is increased).
i. Shorter
ii. Longer
iii. Unchanged
Explanation:
3. Consider the frequency of the sound pro
T^2 = 4*pi^2(L/g)
1a. Longer. A smaller g increases the ratio of L/g which increases the
period.
1b. Unchanged. The mass is not included in the Eq.
1c. Shorter. The ratio of L/g decreases which decreases the period.
1d. Unchanged. The ratio of L/g remains the same. Therefore, the period remains the same.
a. The pendulum is transported to another planet where the acceleration due to gravity is smaller.
i. Shorter
Explanation: The oscillation period of a pendulum is determined by the length of the pendulum and the acceleration due to gravity. Since the acceleration due to gravity is smaller on another planet, the oscillation period will be shorter.
b. The mass of the pendulum increases.
ii. Longer
Explanation: The oscillation period of a pendulum is independent of the mass. Therefore, increasing the mass of the pendulum will have no effect on the oscillation period.
c. The length of the pendulum decreases (i.e., the pendulum arm is shortened).
iv. Shorter
Explanation: The oscillation period of a pendulum is directly proportional to the square root of the length of the pendulum. Therefore, decreasing the length of the pendulum will result in a shorter oscillation period.
d. The distance the pendulum travels or how far it travels from side to side (i.e., the amplitude of oscillation) is reduced.
iii. Unchanged
Explanation: The oscillation period of a pendulum is unaffected by the amplitude of oscillation. Therefore, reducing the amplitude will have no effect on the oscillation period.
2. Consider a block attached to a spring shown in Figure 9.1.5 of the textbook.
a. The mass of the block is reduced.
iii. Unchanged
Explanation: The oscillation period of a block attached to a spring is independent of the mass of the block. Therefore, reducing the mass of the block will have no effect on the oscillation period.
b. The spring – mass device is transported to the Moon, where the acceleration due to gravity is weaker.
iii. Unchanged
Explanation: The oscillation period of a block attached to a spring is determined by the mass of the block and the spring constant of the spring, but not the acceleration due to gravity. Therefore, transporting the device to the Moon will have no effect on the oscillation period.
c. The stiffness of the spring is reduced (i.e., the spring constant is lowered).
ii. Longer
Explanation: The oscillation period of a block attached to a spring is inversely proportional to the square root of the spring constant. Therefore, reducing the spring constant will result in a longer oscillation period.
d. The amplitude of the oscillation is increased (i.e., the distance the mass travels up and down is increased).
iii. Unchanged
Explanation: The oscillation period of a block attached to a spring is independent of the amplitude of oscillation. Therefore, increasing the amplitude will have no effect on the oscillation period.
3. Consider the frequency of the sound pro