Question

Time period of a simple pendulum is 2s. Find its frequency?
(A) 0.5 Hz
(B) 1 Hz
(C) 1.5 Hz
(D) 2 Hz

Answer 1

Hint: Frequency is defined as the inverse of time period. $f = \dfrac{1}{T}$ , where f denotes the frequency of oscillation and T denotes the time period of oscillation. Using this formula, we can calculate frequency, since Time period is given in the question.

Complete step by step solution:
The time period of oscillation means the time in which a simple pendulum completes one oscillation and frequency of oscillation means the number of oscillations the pendulum will perform in one second. From the above statement we can relate frequency and time period according to the relation
$f = \dfrac{1}{T}$.
Using T = 2 seconds, we get
$f = \dfrac{1}{2}$ ,

Hence, $f = 0.5Hz$.

Therefore, the correct answer to the question is option : A

Additional information: The angular frequency of oscillations can also be calculated using only time period, the angular frequency is related to time period according to the relation $\omega = \dfrac{{2\pi }}{T}$.
The time period of oscillations of a simple pendulum or any simple harmonic oscillation is independent of the amplitude of oscillations, hence even if a pendulum is made to swing in a bigger amplitude, the time period, frequency and angular frequency remains same.
The time period of a simple pendulum is calculated by the formula $T = 2\pi \sqrt {\dfrac{l}{g}} $, where l denotes the length of the wire of the simple pendulum and g is acceleration due to gravity at the place where the experiment is being performed.

Note: Before attempting to solve the problem, the student needs to be able to understand the fundamentals of oscillations. This relation between frequency and time period is general and can be used beyond the cases of simple harmonic motion.