Question

The period of a simple pendulum is 2.05s, What is the period of another simple pendulum which makes 300vibrations in the time it takes the first pendulum to make 200 vibration

Answer 1

Let's first find the time that the first pendulum takes to make 200 vibrations:

$$T_1=\dfrac{t_1}{Number\ of\ vibrations},$$ $$t_1=200T_1=200\cdot2.05\ s=410\ s.$$

Since we know from conditions of the question that $t_1=t_2=t$, we can find the period of the second pendulum from the same formula:

$$T_2=\dfrac{t_2}{Number\ of\ vibrations}=\dfrac{410\ s}{300}=1.36\ s.$$

Answer:

$T_2=1.36\ s.$