Question

Figure shows the position-time graph of an object in S.H.M. The correct equation representing this motion is

• A. $2 \sin \left(\frac{2 \pi}{5} t+\frac{\pi}{6}\right)$
• B. $4 \sin \left(\frac{\pi}{5} t+\frac{\pi}{6}\right)$
• C. $4 \sin \left(\frac{\pi}{6} t+\frac{\pi}{3}\right)$
• D. $4 \sin \left(\frac{\pi}{6} t+\frac{\pi}{6}\right)$

Answer 1

Answer: (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 $x=\left(\frac{\pi}{6} t+\frac{\pi}{6}\right)$