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
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
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The restoring force equals k times displacement, and acceleration equals force over mass.
Updated On: Oct 1, 2026
- \(\frac{1}{\sqrt{2}}\)
- \(\sqrt{2}\)
- \(2\)
- \(2\sqrt{2}\)
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The Correct Option is D
Solution and Explanation
Step 1: Force constant:
Restoring force \(F = kx\). With \(F = 0.4\) N and \(x = 4\) cm \(= 0.04\) m:
\[ k = \frac{0.4}{0.04} = 10\text{ N/m} \]
Step 2: Acceleration:
\[ a = \frac Fm = \frac{0.4}{0.4} = 1\text{ m/s}^2 \]
So the force constant is 10 N/m and the acceleration is 1 m/s\(^2\) at that displacement.
Final Answer:
The force constant is 10 N/m and the acceleration is 1 m/s\(^2\), option (B). \[ \boxed{10\text{ N/m},\ 1\text{ m/s}^2} \]
Restoring force \(F = kx\). With \(F = 0.4\) N and \(x = 4\) cm \(= 0.04\) m:
\[ k = \frac{0.4}{0.04} = 10\text{ N/m} \]
Step 2: Acceleration:
\[ a = \frac Fm = \frac{0.4}{0.4} = 1\text{ m/s}^2 \]
So the force constant is 10 N/m and the acceleration is 1 m/s\(^2\) at that displacement.
Final Answer:
The force constant is 10 N/m and the acceleration is 1 m/s\(^2\), option (B). \[ \boxed{10\text{ N/m},\ 1\text{ m/s}^2} \]
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