Question

A simple pendulum makes 20 oscillations in 40 seconds. what is the time period and frequency of its oscillations? i need full explanation with the method ok plz

Answer 1

Given :

No. of oscillations in 40 seconds = 20

To Find :

Time period and Frequency of the oscillation

Solution :

Time Period (T) - Time period of oscillation of a vibrating particle is defined as the time taken by it to execute one complete oscillation.

Time for completing 20 oscillations = 40 seconds

Time for completing 1 oscillation = $\frac{40}{20}$ = 2 seconds

∴ Time period of the oscillation is 2 seconds.

Frequency (n) - Frequency of oscillation of a vibrating particle is defined as the number of complete oscillations executed by it in 1 second. It is inverse of the time period.

We know, Frequency = $\frac{1}{Time Period}$

                                    = $\frac{1}{2}$

                                    = 0.5 Hz

∴ The Frequency of the simple pendulum is 0.5 Hz.

Answer 2

Given:

Oscillations in time duration 40 seconds = 20

To Find: Time period and Frequency of pendulum

Calculation:

• Time-period is the time taken by a wave to complete one oscillation.
• 20 oscillation takes = 40 seconds
• 1 oscillation takes = $\frac{40}{20}$ seconds = 2 seconds
• So, the time taken to complete one oscillation = 2 s
• Frequency is reciprocal of time period. Frequency is given as $f=\frac{1}{T}$.
• $f=\frac{1}{T} =\frac{1}{2} =0.5 Hz$

Answer:

Time period is 2 seconds and oscillation is 0.5 Hz.