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  4. The displacement y(t)=A sin(ω t+φ) of a pendulum for φ=(2π/3) is correctly represented by

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Q. The displacement $y\left(t\right)=A\,sin\left(\omega t+\phi\right)$ of a pendulum for $\phi=\frac{2\pi}{3}$ is correctly represented by

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Solution:

Displacement $y\left(t\right)=A\,sin\,\left(wt+\phi\right)$
[Given]
For $\phi=\frac{2\pi}{3}
at t=0; y=A\,sin\,\phi=A\,sin \frac{2\pi}{3}$
$=A\,sin\,120^{\circ}=0.87\,A\left[\because\,sin\,120^{\circ}\simeq0.866\right]$
Graph (a) depicts $y = 0.87$ at $t=0$