Question

A pendulum is vibrating in a viscous medium. The amplitude of vibrations becomes $\frac { 1 } { 2 }$ after 40 seconds. 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

Q A² = A₀² e^–lt

$\left( \frac { \mathrm { A } _ { 0 } } { 2 } \right) ^ { 2 }$ = A₀² e^–l(40) so e^–40l = $\frac { 1 } { 4 }$ …..(1)

$\left( \frac { \mathrm { A } _ { 0 } } { 8 } \right) ^ { 2 }$ = A₀² e^–lt, $\frac { 1 } { 64 }$ = e^–lt

̃ $\left( \frac { 1 } { 4 } \right) ^ { 3 }$ = e^–lt (e^–40l)³ = – lt , t = 120 sec

so 120 sec