Answer:
2. Using a shorter string of length L ′ ≈ 0.25 meters
5. Using a shorter string of length L ′ ≈ 0.5 meters
Explanation:
The period of a pendulum is given by
where
L is the length of the pendulum
g is the acceleration due to gravity
We see from the formula that the period of the pendulum depends only on its length, not on its mass or its amplitude of ocillation. Therefore, the only alterations that can change the period of the pendulum are the ones where its length is changed.
Moreover, we notice that the period is proportional to the square of the length: this means that in order to decrease the period of the pendulum (the problem asks us which alterations will reduce the period of the pendulum from 2 s to 1 s), the length of the pendulum should also be reduced.
Therefore, the only alterations that will reduce the period of the pendulum are:
2. Using a shorter string of length L ′ ≈ 0.25 meters
5. Using a shorter string of length L ′ ≈ 0.5 meters