JEE PYQ: Oscillations Question 2
Question 2 - 2021 (16 Mar 2021 Shift 2)
Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass $= 500$ g, 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? ($\ln 2 = 0.693$)
(1) 34.65 s
(2) 17.32 s
(3) 0.034 s
(4) 15.01 s
Show Answer
Answer: (1)
Solution
$A = A_0 e^{-\frac{bt}{2m}}$. $\frac{A_0}{2} = A_0 e^{-\frac{bt}{2m}}$. $t = \frac{2m}{b}\ln 2 = \frac{2 \times 500 \times 0.693}{20} = 34.65$ s.
BETA
