Question

A simple pendulum takes \[32s\] to complete 20 oscillations, what is the time period of the pendulum?

Answer 1

Hint: Time period of a pendulum is time taken by it to complete 1 oscillation.

Complete step by step solution:
Time taken by the pendulum to complete 20 oscillations = $32\,s$
Time taken by the pendulum to complete 1 oscillation = \[\dfrac{{32}}{{20}}\,s = 1.6\,s\]

Hence, the time period of the pendulum is 1.6 seconds.

Additional Information: A simple pendulum consists of a mass m hanging from a string of length  l and fixed at a pivot point. When it is displaced to an initial angle and released, the pendulum will swing back and forth with periodic motion. The time taken by the pendulum to complete one back and forth motion is called its time period. The number of oscillations made by a pendulum in one second is called its frequency. The time period of a pendulum is given by the equation $T = 2\pi \sqrt {\dfrac{l}{g}} $ . The time period of a simple pendulum does not depend on the mass or the initial angular displacement, but depends only on the length of the string and the value of the gravitational field strength g . If the temperature of a system changes then the time period of the simple pendulum changes due to change in length of the pendulum.

Note: The maximum displacement made by a pendulum on either side is called its amplitude. If the amplitude of a simple pendulum is kept small, it will execute simple harmonic motion. A simple pendulum has many applications in real life, for example it is used in clocks whose time period is kept 1 seconds.