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: Time to reach \(\frac A2\)
With \(x=A\sin\omega t\), \(x=\frac A2\) when \(\omega t=\frac\pi6\), so \(t=\frac{T}{12}\).

Step 2: Find \(T\)
\(\frac{T}{12}=2\) s gives \(T=24\) s.

Step 3: Time from \(\frac A2\) to \(A\)
Time from \(0\) to \(A\) is \(\frac T4=6\) s. So the time from \(\frac A2\) to \(A\) is \(6-2=4\) s. Option (D).

Final Answer:
The time is \(4\) s, option (D). \[ \boxed{\text{(D) }4\text{ s}} \]