Amplitude of Mass Spring System...... | JEE Main 2021 | SHM

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JEE MAIN 2021

16-03-2021 S2

Question

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500g, Decay constant = 20 g/s then how much time is required for the amplitude of the system to drop to half of its initial value? (ln 2 = 0.693)

Select the correct option:

A

34.65 s

B

17.32 s

C

0.034 s

D

15.01 s

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & A=A_0 e^{-\gamma t}=A_0 e^{-\frac{b t}{2 m}} \\ & \frac{A_0}{2}=A_0 e^{-\frac{b t}{2 m}} \\ & \frac{b t}{2 m}=\ln 2 \\ & t=\frac{2 m}{b} \ln 2=\frac{2 \times 500 \times 0.693}{20} \\ & T=34.65 \text { second. }\end{aligned}$

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