The amplitude of a damped harmonic oscillator becomes $50 \%$ of its initial value in a time of $12 \ s$. If the amplitude of the oscillator at a time of $36 \ s$ is $x \%$ of its initial amplitude,then the value of $x$ is

$A$ particle is performing simple harmonic motion. If the oscillations are damped oscillations,then the angular frequency is given by:

$A$ block of mass $0.1\, kg$ is connected to an elastic spring of spring constant $640\, Nm^{-1}$ and oscillates in a damping medium of damping constant $10^{-2}\, kg\,s^{-1}$. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value is closest to ..... $s$.

The amplitude of a damped oscillator becomes half in $1$ minute. The amplitude after $3$ minutes will be $\frac{1}{x}$ times the original. Then $x$ is

Resonance is an example of

$A$ spring-mass system executes damped harmonic oscillations given by the equation $y = A e^{-\frac{bt}{2m}} \sin(\omega' t + \phi)$,where the symbols have their usual meanings. If a $2 \ kg$ mass $(m)$ is attached to a spring of force constant $(K) = 1250 \ N/m$,the period of the oscillation is $(\pi / 12) \ s$. The damping constant $b$ has the value ..... $kg/s$.