Question

Calculate the time-period and frequency if a pendulum completes 20 oscillations in 4s.

Answer 1

Explanation:

20 oscillations in 4 sec

1 oscillation in 4/20 Sec

So Time Period = 1/5 Sec

And Frequency = 1/ Time Period

F = 5 Hz

Answer 2

Given :-

Number of oscillations taken by the pendulum = 20

Time taken by the pendulum = 4 sec

To Find :-

The time period.

The frequency.

Analysis :-

Here we are given with the number of oscillations and the time taken.

Using it's respective formulas, substitute the values given and find the answers accordingly for the same.

Solution :-

We know that,

• n = No. of oscillation
• t = Time
• f = Frequency
• T = Time period

Using the formula,

$\underline{\boxed{\sf Frequency=\dfrac{Number \ of \ oscillations}{Time \ taken} }}$

Given that,

Number of oscillations (n) = 20

Time (t) = 4 sec

Substituting their values,

⇒ f = 20/4

⇒ f = 5 Hz

Therefore, the time frequency is 5 Hz.

Using the formula,

$\underline{\boxed{\sf Time \ period=\dfrac{1}{Frequency} }}$

Given that,

Frequency (f) = 5 Hz

Substituting their values,

⇒ T = 1/5

⇒ T = 0.2 sec

Therefore, the time period is 0.2 sec.