Question

A body of mass $0.01\text{kg}$ executes simple harmonic motion (SHM) about $x=0$ under the influence of a force $F$ which varies with $x$ as shown in figure. Find the time period of SHM of the body.

• A. $\frac{\pi }{5}$
• B. $\frac{\pi }{10}$
• C. $\frac{3\pi }{10}$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is B $\frac{\pi }{10}$

From the graph, we can deduce that the $F-x$ graph is a straight line passing through the origin.
Slope of $F-x$ curve gives
$-k=\frac{F_2-F_1}{x_2-x_1}=\frac{8-0}{0-2}\Rightarrow k=4$
Time period of oscillation of the body is given by,
$T=2\pi \sqrt{\frac{m}{k}}$
From the data given in the question,
$T=2\pi \sqrt{\frac{0.01}{4}}=2\pi \times \frac{0.1}{2}=\frac{\pi }{10}\text{s}$
Thus, option (b) is the correct answer.