91Ó°ÊÓ

A pendulum by graphing the angle \(\theta \) that the string makes with the vertical as a function of time \(t\)

The letter "\(T\)" stands for the period of time needed for the pendulum to complete one complete oscillation.

\(T = 2\pi \sqrt {\frac{L}{g}} \) …(i)

Where, \(L\) is the length of pendulum and \(g\) is the acceleration due to gravity

From the graph, the distance between two consecutive troughs or two consecutive valley will give the time period.

So, from the graph time period is \(T = 1.6\,{\rm{s}}\)

Frequency of the pendulum is expressed as,

\(f = \frac{1}{T}\)

Substitute \(T = 1.6\,{\rm{s}}\) in above equation

\(\begin{array}{c}f = \frac{1}{{1.6\,{\rm{s}}}}\\ = 0.625\,{\rm{Hz}}\end{array}\)

Hence, the frequency of pendulum is \(0.625\,{\rm{Hz}}\)

Angular frequency of the pendulum is expressed as,

\(\omega = 2\pi f\)

Substitute \(f = 0.625\,{\rm{Hz}}\) in above equation

\(\begin{array}{c}\omega = 2\pi \times 0.625\,{\rm{Hz}}\\ = 3.93\,{\rm{rad/s}}\end{array}\)

Hence, the angular frequency of pendulum is \(3.93\,{\rm{rad/s}}\)

Amplitude of the pendulum’s motion is maximum displacement in the y-axis in the graph.

From graph the amplitude of the pendulum’s motion is \({6^o}\)