Question

The figure shows the displacement time graph of a particle executing S.H.M. If the time period of oscillation is $2$s the equation of motion of its S.H.M. is:

• A. $x=10\sin \left(\pi t+\pi /3\right)$
• B. $x=10\sin \left(\pi t\right)$
• C. $x=10\sin \left(\pi t+\pi /6\right)$
• D. $x=10\sin \left(2\pi t+\pi /6\right)$

Answer 1

The correct option is C $x=10\sin \left(\pi t+\pi /6\right)$

A = amplitude = 10

T = 2 src $=\frac{2\pi }{\omega }$

$\omega =\pi$

Let, equations,

$x=10sim(\pi t+\varphi )$

at, $t=0,x=S$

$\frac{1}{2}=sin\left(\varphi \right)$

$\varphi =\frac{\pi }{10}$

So, $x=10sin(\pi t+\pi /10)$