Question

What is the length of a simple pendulum whose full swing from left to right and then back again takes 3.2 S?

Short answer

The length of a simple pendulum is 2.54.

Step-by-step solution

The given data

Full swing time is3.2 s .

Understanding the concept of the period of Simple Harmonic Motion

Using the formula for the period of a simple pendulum, we can find the length of a simple pendulum.

Formula:

The time period of a simple pendulum in SHM,

$T=2\pi \sqrt{\frac{L}{g}}$

Calculation of the length of the pendulum

Using equation (i), we have the value of the length of the pendulum as:
$$\begin{gathered} L=\frac{T^{2}g}{4\pi } \\ =\frac{3.2s^2\times 9.8m/s^2}{4{\pi }^2} \\ =2.54m \end{gathered}$$

Hence, the required value of length is 2.54m.