Question

A body of mass \(0.4\) kg performs simple harmonic motion. It experiences a restoring force of \(0.4\) N when its displacement from the mean position is 4 cm. The force constant and magnitude of acceleration respectively are

• A. \(5 \text{N/}_{\text{m}},0.5 \text{m/}_{\text{s}^2}\)
• B. \(10 \text{N/}_{\text{m}},1 \text{m/}_{\text{s}^2}\)
• C. \(15 \text{N/}_{\text{m}},1.5 \text{m/}_{\text{s}^2}\)
• D. \(20 \text{N/}_{\text{m}},2 \text{m/}_{\text{s}^2}\)

Hint:

k = F / x and a = F / m.

Answer 1

The Correct Option is B

Step 1: Convert
$x = 4$ cm $= 0.04$ m.

Step 2: Spring constant
$k = 0.4/0.04 = 10$ N/m.

Step 3: Acceleration
$a = 0.4/0.4 = 1$ m/s$^2$. Option (B).

Final Answer:
Option (B). \[ \boxed{10 \text{ N/m},\ 1 \text{ m/s}^2} \]