Question

A simple pendulum completes 420 oscillations in 2 minutes.
Calculate its frequency and time period.

Answer 1

Answer:

frequency= 0.667 Hz

timeperiod= 1.5 sec

Explanation:

Number of Oscillations, N=40

Time t=1min

Frequency f=  n/t = 40/60 = 0.667 Hz

Time period,T= 1/f = 1.5 sec

Hence, frequency is 0.667Hz and time period is 1.5sec

Answer 2

Answer:

A simple pendulum completes 420 oscillations in 2 minutes.

Frequency     = $3.5Hz$

Time period   = $0.2857s$

Explanation:

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

• The expression for the time period is given by,

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

• The number of oscillations completed per time is the frequency of oscillation. It can be expressed as,  

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

         So as per definition,

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

         and

        $T = \frac{1}{f}$

• In the question, it is given that,

        N   $=420$

         t   $=2 min = 2\times 60s = 120s$

• Then using equation(1),

         f = $\frac{420}{120} =3.5 Hz$

         T = $\frac{1}{3.5}= 0.2857s$