A pendulum oscillates 40 times in 4 seconds. Find its time period and frequency

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Solution

Step (1) Given:
No. of oscillations, $v = 40$
Time taken, $t = 4 s e c o n d s .$
Step (2) Finding the time period, T using the formula:
We know that time period, $T = \frac{t i m e t a k e n f o r n o . o f o s c i l l a t i o n s}{n o . o f o s c i l l a t i o n s .}$
The time period, $T$ of the given pendulum, is
$= \frac{4}{40} = \frac{1}{10} t h o f a s e c o n d .$
Therefore, the time period of the given pendulum is $\frac{1}{10} s e c (o r) 0.1 s e c$
Step (3): Finding the frequency, $v$ of the pendulum:
We know that
$F r e q u e n c y = \frac{(N u m b e r o f O s c i l l a t i o n s)}{(T i m e t a k e n)} F r e q u e n c y o f t h e g i v e n p e n d u l u m = (\frac{40}{4}) = 10 H z .$
Hence, the frequency of the given pendulum is 10 Hz.

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