A block of mass 1 kg attached to a spring is made to oscillate
Question:

A block of mass $1 \mathrm{~kg}$ attached to a spring is made to oscillate with an initial amplitude of

$12 \mathrm{~cm}$. After 2 minutes the amplitude decreases

to $6 \mathrm{~cm}$. Determine the value of the damping

constant for this motion. (take In $2=0.693$ )

1. (1) $0.69 \times 10^{2} \mathrm{~kg} \mathrm{~s}^{-1}$

2. (2) $3.3 \times 10^{2} \mathrm{~kg} \mathrm{~s}^{-1}$

3. (3) $1.16 \times 10^{-2} \mathrm{~kg} \mathrm{~s}^{-1}$

4. (4) $5.7 \times 10^{-3} \mathrm{~kg} \mathrm{~s}^{-1}$

Correct Option: , 3

Solution:

(3)

$\mathrm{A}=\mathrm{A}_{0} \mathrm{e}^{-\gamma t}$

$\ln 2=\frac{\mathrm{b}}{2 \mathrm{~m}} \times 120$

$\frac{0.693 \times 2 \times 1}{120}=\mathrm{b}$

$1.16 \times 10^{-2} \mathrm{~kg} / \mathrm{sec}$