Question

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

• A. $1.05\text{s}$
• B. $0.52\text{s}$
• C. $0.25\text{s}$
• D. $0.31\text{s}$

Answer 1

The correct option is D $0.31\text{s}$

From the graph, we can see that :
$F=-Kx$
$\Rightarrow$Slope of graph :
Slope = $(-K)=\frac{\Delta F}{\Delta x}=\frac{8}{-2}=-4$
$\Rightarrow K=4$
Time period of SHM $\left(T\right)=2\pi \sqrt{\frac{m}{K}}$
$=2\times 3.14\times \sqrt{\frac{0.01}{4}}$
$=0.31\text{s}$