Question

A particle executes simple harmonic motion between \(x = -A\) and \(x = +A\). If time taken by particle to go from \(x = 0\) to \(\frac{A}{2}\) is \(2\)s, then time taken by particle in going from \(x = \frac{A}{2}\) to A is

• A. \(3\) s
• B. \(2\) s
• C. \(1.5\) s
• D. \(4\) s

Hint:

Use $x=A\sin\omega t$ to find the time to reach $A/2$.

Answer 1

The Correct Option is D

Step 1: Phase angles
$\frac A2$ is at phase $30^{\circ}$ and $A$ is at $90^{\circ}$. The first stretch covers $30^{\circ}$ in $2$ s, so the second stretch covers $60^{\circ}$, which takes $4$ s.

Final Answer:
Option (D). \[ \boxed{\text{(D)}} \]