Question

A pendulum oscillates 40 times in 4 seconds. The time period of vibration will be

Answer 1

Frequency = (Number of Oscillations)/Time = 40/4 = 10 Hz

The time required to complete one oscillation is known as time period. It is given by the inverse of the frequency.

Time period = 1/(Frequency of Oscillation) = 1/10 = 0.1 sec.

Answer 2

Answer:

A pendulum oscillates 40 times in 4 seconds. The time period of vibration will be $0.1\ s$

Explanation:

The frequency of oscillations of a vibrating body can be defined as the number of oscillations of that body per second.

It is given by,

$Frequency\ (f) = \frac{Number\ of\ oscillations\ (N)}{Time\ (t)}$     ...(1)

The inverse of the frequency is the time period of the oscillating body. Or in other words, the time required to complete one oscillation is known as the time period.  

That is,

$Time\ period\ (T)= \frac{1}{f}$      ...(2)

In the question, it is given that,

$N = 40$

$t = 4\ s$

Substituting these values into equation (1) and equation (2)

$f = \frac{40}{4} = 10\ Hz$

Now,

$T = \frac{1}{10} = 0.1\ s$