Question

A simple pendulum takes 13 seconds to complete 26 oscillations. Calculate its frequency and
time period

Answer 1

Answer:

Time period of pendulum is 1.6 seconds.

Answer 2

Answer:

A simple pendulum takes 13 seconds to complete 26 oscillations. Its frequency is 2Hz and the time period is 0.5s

Explanation:

• For a simple pendulum, the number of oscillations completed per time is the frequency of oscillation. It can be obtained by the equation,  

        $Frequency = \frac{No\ of\ oscillations}{time\ taken}$

        The time period of an oscillation can be expressed as,

        $Time\ period = \frac{1}{frequency}$

• Let f be the frequency of oscillation, N be the number of oscillations completed in time t and T be the time period.

         So as per definition,

        $f = \frac{N}{t}$                            ...(1)

         and

        $T = \frac{1}{f}$

• In the question, it is given that,

        N   $=26$

         t   $=13s$

• Then using equation(1),

         f = $\frac{26}{13} =2 Hz$

         T = $\frac{1}{2}= 0.5s$