A vibrating system consists of mass 12.5 kg, a spring of spring constant 1000 ` (N ) /( m ) ` performing damped oscillation with damping coefficient of 15 kg `s^(-1)`. The value of critical damping coefficient of the system is

Options

A. ` 223.6 kg s ^( - 1 ) `
B. `71.4 kg s ^( - 1 ) `
C. `100 kg s ^( - 1 ) `
D. `110 kg s ^( - 1 ) `

Answer

A

Explanation

` m = 12.5 ` kg
` k = 1000 ( N ) /( m ) `
` b = 15 kg s ^( - 1 ) `
We know that at critical damping
` omega = (b _ c)/ ( 2m ) `
` b _ c = omega 2m = sqrt((k)/(m)) 2m `
` b _ c = 2 sqrt ( m k ) `
` b _ c = 2 sqrt( 12.5 xx 1000) `
` b _ c = 223.6 kg s ^( - 1 ) `