Question

A simple harmonic motion has an amplitude A & time period T. The time required by it to travel from $x=Atox=\frac{A}{2}$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Time required to travel from x = A to x = 0 is $\frac{T}{4}$ & time required to travel from $x=\frac{A}{2}tox=0$ is equal to the time required to travel from $x=0tox=\frac{A}{2}$ which is obtained from
$y=A\sin \left(\frac{2\pi }{T}\right)t\frac{A}{2}=A\sin \left(\frac{2\pi }{T}\right)t\Rightarrow \sin \left(\frac{\pi }{6}\right)=\sin \left(\frac{2\pi }{T}\right)t\Rightarrow t=\frac{T}{12}\Rightarrow Timerequiredtotravelfromx=Atox=\frac{A}{2}willbe\frac{T}{4}-\frac{T}{12}=\frac{T}{6}\therefore \left(A\right)$