The equation of a damped simple harmonic motion is `2m(d^(2)x)/(dt^(2))+2a_(0)(dx)/(dt)+kx=0`. Then the angualr frequency of oscillation is

Options

A. `omega=((k)/(m)-(a_(0)^(2))/(2m^(2)))^(1//2)`
B. `omega=((k)/(m)-(a_(0))/(4m))^(1//2)`
C. `omega=((k)/(2m)-(a_(0)^(2))/(4m^(2)))^(1//2)`
D. `omega=((k)/(m)-(a_(0)^(2))/(4m^(2)))^(1//2)`

Answer

C

Explanation

Displacement of damped oscillator is given by
`x=x_(m)e^((2a_(0))/(4m))sin(omega't+phi)` where
`omega'=`angular frequency of damped oscillator.
`sqrt(omega_(0)^(2)-((2a_(0))/(2m))^(2))=sqrt((k)/(2m)-(4a_(0)^(2))/(16m^(2)))`
`=sqrt((k)/(2m)-(a_(0)^(2))/(4m^(2)))`