Question

A simple harmonic motion has an amplitude '$a$' and time period $T$ Find the time required to travel From $y=a$ to $y=\frac{a}{2}$

• A. $\frac{T}{6}$
• B. $\frac{T}{12}$
• C. $\frac{T}{10}$
• D. $\frac{T}{9}$

Answer 1

Answer: (A)

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 $y=a\sin wt$
$\Rightarrow \frac{a}{2}=a\sin \frac{2\pi }{T}\cdot t$
$\Rightarrow \sin \frac{\pi }{6}=\sin \frac{2\pi }{T}\cdot t$
$\Rightarrow \frac{\pi }{6}=\frac{2\pi }{T}\Rightarrow t=\frac{T}{12}$
Time required to travel from $y=a$ to $y=\frac{a}{2}$ is
$=\frac{T}{4}-\frac{T}{12}=\frac{T}{6}$