Question

The acceleration-displacement graph of a particle executing SHM is shown in given figure. The time period of its oscillation in seconds is

• A. $\frac{\pi }{2}$
• B. $2\pi$
• C. $\pi$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is B $2\pi$

Acceleration of a particle executing SHM is given by
$a=-{\omega }^{2}x$
So, from the graph, we get
$-{\omega }^2=\tan (\pi -{45}^{\circ })=-1$ (Slope of the graph)
$\Rightarrow {\omega }^2=1$
$\Rightarrow \frac{2\pi }{T}=\omega =1$
$\Rightarrow T=2\pi \text{s}$