Question

The displacement of a particle performing linear S.H.M. is given by \(y = Acos[π(t+φ)]\). If at \(t = 0\), the displacement is \(y = 2\) cm and velocity is \(2π\) cm/s, the value of amplitude A in cm is

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

Hint:

The restoring force equals k times displacement, and acceleration equals force over mass.

Answer 1

The Correct Option is D

Step 1: Using omega squared:
$a = \omega^2x$ and $\omega^2 = \frac km$. First $k = \frac Fx = 10$ N/m.

Step 2: Then:
$\omega^2 = \frac{10}{0.4} = 25$, so $a = 25\times0.04 = 1$ m/s$^2$ (B).

Final Answer:
10 N/m and 1 m/s squared. \[ \boxed{10\text{ N/m},\ 1\text{ m/s}^2} \]