Question

A pendulum is vibrating in a medium. The amplitude of vibrations becomes $\frac{1}{2}$after 40 sec. Its amplitude will be $\frac{1}{8}$of its initial amplitude after –

• A. 80 seconds
• B. 120 seconds
• C. 40 seconds
• D. 160 seconds

Answer 1

Answer: (B)

120 seconds

Answer 2

A² = $\mathrm { A } _ { 0 } ^ { 2 }$ e^{– lt}

$\left( \frac { \mathrm { A } _ { 0 } } { 2 } \right) ^ { 2 }$ = $\mathrm { A } _ { 0 } ^ { 2 }$ e^{– 40l} …………(1)

$\left( \frac { \mathrm { A } _ { 0 } } { 8 } \right) ^ { 2 }$ = $\mathrm { A } _ { 0 } ^ { 2 }$ e^{– lt} …………(2)

so by (1) and (2)

3 × 40 = t

t = 120 sec