Question

A pendulum is vibrating in a viscous medium. The amplitude of vibration becomes $\frac { 1 } { 2 }$ after 40 second. Its amplitude will be $\frac { 1 } { 8 }$ of its initial amplitude after -

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

Answer 1

Answer: (B)

120 sec.

Answer 2

$\left( \frac { 1 } { 2 } \right) ^ { 2 } = \mathrm { e } ^ { - 40 \lambda }$ , $\frac { 1 } { 2 }$ = e^–20l

$\left( \frac { 1 } { 8 } \right) ^ { 2 }$ = e^–lt, $\left( \frac { 1 } { 2 } \right) ^ { 6 }$ = e^–lt so e^{– 20l ×6}

= e ^–lt or t = 120 sec.