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:
All explanations on the base of formula for period os spring pendulum
T=2πsqrt(m/k)
(a) m↓=>T↓
i. Shorter
(b) iii. Unchanged
(c) k↑↓ => T
ii. Longer
(d) iii. Unchanged
a. The mass of the block is reduced.
Answer: shorter
Explanation: When the mass of the block is reduced, the oscillation period becomes shorter. This is because the block requires less force to move back and forth due to its reduced mass. As a result, it can accelerate and decelerate more quickly, leading to a shorter period of oscillation.
b. The spring – mass device is transported to the Moon, where the acceleration due to gravity is weaker.
Answer: longer
Explanation: When the spring-mass device is transported to the Moon, where the acceleration due to gravity is weaker than on Earth, the oscillation period becomes longer. This is because the force of gravity acting on the block is reduced, resulting in a weaker restoring force from the spring. As a result, the block takes longer to complete each oscillation, leading to a longer period.
c. The stiffness of the spring is reduced (i.e., the spring constant is lowered).
Answer: longer
Explanation: When the stiffness of the spring is reduced, or the spring constant is lowered, the oscillation period becomes longer. This is because a lower spring constant means that the spring is less resistant to deformation. As a result, the block can move more easily, leading to a longer period of oscillation.
d. The amplitude of the oscillation is increased (i.e., the distance the mass travels up and down is increased).
Answer: unchanged
Explanation: The amplitude of the oscillation, which represents the distance the mass travels up and down, does not affect the period of oscillation. The period is determined by the mass of the block, the spring constant, and the force that acts on the block. Therefore, increasing the amplitude does not change the balance between these factors and thus does not change the period of oscillation.