Question

A pendulum oscillates 40 times in 4 minutes. Find time period and frequency.

Answer 1

You can use the number of oscillations formed in 4 minutes to calculate the time required for one complete oscillation. You need to convert the units of time into seconds. You can calculate frequency by taking a reciprocal of time period. The unit of frequency is Hertz.

Formula used:
Time period, $T=\dfrac{t}{N}$
Frequency, $f=\dfrac{1}{T}$

Complete step-by-step answer:
We are given that a pendulum oscillates for 40 times in 4 minutes.
Time period (T) of a simple pendulum means the time required by it to complete one oscillation.
$T=\dfrac{t}{N}$ , where t is total time and N is total number of oscillations
$\Rightarrow T=\dfrac{4\times 60}{40}=6s$.
Frequency (f) of a simple pendulum is the reciprocal of its time period.
$f=\dfrac{1}{T}$
$f=\dfrac{1}{6}=0.167$ Hz
Hence the time period of the pendulum is 6s and the frequency of the pendulum is 0.167Hz.

Additional information:
A pendulum is a weight suspended from a rigid support using a string or a metallic rod. It can be set in motion by displacing the bob to an extreme position and leaving it. The first scientific experimentation was done by Galileo Galilei. The movement of the pendulum was used for knowing time. It was the best time keeper till the 1930s. There are different types of pendulums apart from the simple pendulum. They are used in various fields apart from timekeeping like temperature compensation, pressure measurement and reading gravity.

Note: Instead of vertical pendulums, the pendulum rod is placed horizontal and was earlier used as seismographs for measuring earth’s tremor. When a rigid swinging body is free to rotate on its horizontal axis it is called a compound pendulum or physical pendulum. The proper length of this pendulum is the distance from the pivot to the center of oscillation.