A body of mass 0.3 kg hangs by a spring with force constant of 50 N/m . The amplitude of oscillations is damped and reaches `1/e` of its original value in about 100 oscillations. If `omega` and `omega'` are the angular frequencies of undamped and damped oscillations respectively, then percentage of `((omega-omega')/(omega))` is

Options

A. `((1)/(800pi))`
B. `((pi^(2))/(600))`
C. `((1)/(800pi^(2)))`
D. `((pi)/(400))`

Answer

C

Explanation

The displacement of a spring mass oscillator, `X=Ae^(-bt//2m)cos ( omega.t+phi)`
where, `omega.=` angular frequency of damped
oscillation and `omega.=omega_(0)sqrt(1-(b^(2))/(4m^(2)omega_(0)^(2)))`