For the damped oscillator, the mass m of the block is 200g, k = 90 Nm^(-1) and the damping constant b is 40 gs^(-1). Calculate the time taken for its mechanical energy to drop to half its initial value.

For the damped oscillator, the mass m of the block is 200g, k = 90 Nm^

1.	For the damped oscillator, the mass m of the block is 200g, k = 90 Nm^(-1) and the damping constant b is 40 gs^(-1). Calculate the time taken for its mechanical energy to drop to half its initial value.
Answer» Solution :Mechanical energy of a damped oscillatior at time t `THEREFORE E(t)=E_(0)e^((-BT)/(m)" where "E_(0)= (1)/(2) kA^(2)` If `E(t)= (E_0)/(2) implies t= t_(1/2)` `therefore (E_0)/(2)=E_(0)e^(((-bt)_(1/2))/(m))` `therefore 2=e^(((-bt)_(1/2))/(m))` `ln_(2)= (bt)_(1/2)/(m)` `ln_(2)=(ln2xxm)/(b)` `= (0.693xx 200)/(40)` `therefore t_(1/2) = 3.465s`.