If the amplitudes of a damped harmonic oscillator at times $t=0, t_1$ and $t_2$ are $A_0, A_1$ and $A_2$ respectively, then the amplitude of the oscillator at a time of $(t_1+t_2)$ is

$A$ $3 \ kg$ sphere dropped through air has a terminal speed of $25 \ m/s$. (Assume that the drag force is $F_d = -bv$). Now suppose the sphere is attached to a spring of force constant $k = 300 \ N/m$,and that it oscillates with an initial amplitude of $20 \ cm$. What is the angular frequency of its damped $SHM$? ..... $rad/s$

If a damped oscillator is very heavily damped,what is its frequency?

The displacement of a damped harmonic oscillator is given by $x(t) = e^{-0.1 t} \cos(10 \pi t + \varphi)$. Here $t$ is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to: (in $s$)

The time taken for the amplitude of vibrations of a damped oscillator to drop to $25 \%$ of its initial value is $t$. The time taken for its mechanical energy to drop to $50 \%$ of its initial mechanical energy is

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5 \ s$. In another $10 \ s$ it will decrease to $\alpha$ times its original magnitude,where $\alpha$ equals