Figure shows the position-time graph of an object in $S.H.M.$ The correct equation representing this motion is ..........
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(d)
Time period is $12 \,s$ from diagram.
$\omega=\frac{2 \pi}{12}=\frac{\pi}{6}$
Amplitude $A=4$
Initial phase is determined by putting known values in the equation.
$2=4 \sin \left(\frac{\pi}{6} t+\phi\right)$
$\sin ^{-1} \frac{1}{2}=\phi[t=0]$
$\frac{\pi}{6}=\phi$
Hence equation is $x=\left(\frac{\pi}{6} t+\frac{\pi}{6}\right)$
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