Question

A mass attached to a spring performs S.H.M. whose displacement is \(x = 3\times 10^{-3}cos2πt\) m. The time taken to obtain maximum speed for the first time is (in s)

• A. \(1\)
• B. \(\frac{1}{2}\)
• C. \(\frac{1}{4}\)
• D. \(\frac{1}{8}\)

Hint:

Maximum speed occurs at the mean position, where x = 0.

Answer 1

The Correct Option is C

Step 1: Use velocity expression:
$v=\dfrac{dx}{dt}=-3\times10^{-3}(2\pi)\sin2\pi t$. Its magnitude is largest when $|\sin2\pi t|=1$.

Step 2: Find the first time:
$2\pi t=\dfrac\pi2$ gives $t=\dfrac14$ s.

Step 3: Pick:
Option C.

Final Answer:
Maximum speed at x = 0 first occurs after a quarter period, 1/4 s. \[ \boxed{\text{(C) }\dfrac14\ \text{s}} \]