Question

A pendulum has a frequency of 40 times in 4 seconds. Find its time period in seconds.
A) 0.10
B) 0.20
C) 0.30
D) 0.40

Answer 1

The period T is the time it takes the object to complete one oscillation and return to the starting position. And frequency is the inverse of the time period, $T = \dfrac{1}{f}$ . First, calculate the frequency from the given values in the question, and once the frequency is calculated the time period can be calculated easily.

Complete step by step solution:
Step 1: when a pendulum has a frequency of 40 in 4 seconds it means that the pendulum completes 40 cycles in 4 seconds. And frequency is defined as the no. of cycles per unit time. Therefore, to calculate the frequency we will divide the number of total cycles by the time taken. If we denote the frequency by $f$ then
$\therefore f = \dfrac{{cycles}}{{time}}$
Substitute the values.
$\therefore f = \dfrac{{40}}{4}$
$\Rightarrow f = 10Hz$
Therefore, the pendulum completes ten cycles per second.
Step 2: Now write the expression of the relation between time period and frequency.
$\therefore T = \dfrac{1}{f}$
Step 3: substitute the value 10 for $f$ in the above expression
$\therefore T = \dfrac{1}{{10}}$
$\Rightarrow T = 0.1$
Therefore, the time taken by the pendulum to complete one oscillation is 0.1 sec.

Hence the correct option is Option A.

Note: In case if you are given the no. of cycles in a particular time period and you are asked to calculate the time period of one oscillation of the SHM, then simply divide the time period by the no of cycles the result will be time taken by one cycle in the simple harmonic motion. Let us solve the above question.
$T = \dfrac{{time}}{{total{\text{ }}no.{\text{ }}of{\text{ }}cycles}}$
$\Rightarrow T = \dfrac{4}{{40}}$
$\Rightarrow T = 0.1\sec$
Hence the results are the same.