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Q.
A simple harmonic motion has an amplitude '$a$' and time period $T$ Find the time required to travel From $y=a$ to $y=\frac{a}{2}$
Solution:
Time required to travel from $y=a$ to $y=0=\frac{T}{4}$
Time required to travel from $y=0$ to $y=\frac{a}{2}$
is given by $y=a \sin w t $
$\Rightarrow \frac{a}{2}=a \sin \frac{2 \pi}{T} \cdot t$
$\Rightarrow \sin \frac{\pi}{6}=\sin \frac{2 \pi}{T} \cdot t $
$\Rightarrow \frac{\pi}{6}=\frac{2 \pi}{T} \Rightarrow t=\frac{T}{12}$
Time required to travel from $y=a$ to $y=\frac{a}{2}$ is
$=\frac{T}{4}-\frac{T}{12}=\frac{T}{6}$