$A$ simple pendulum is set into vibrations. The bob of the pendulum comes to rest after some time due to

The amplitude of a wave is represented by $A = \frac{c}{a + b - c}$. Resonance will occur when:

The amplitude of a damped oscillator becomes $\left(\frac{1}{3}\right)$ of its original amplitude in $2 \ s$. If its amplitude after $6 \ s$ becomes $\left(\frac{1}{n}\right)$ times the original amplitude,the value of $n$ is ($n$ is a non-zero integer).

In the case of a forced vibration,the resonance curve becomes very sharp when the

The mechanical energy of a damped oscillator becomes half of its initial energy in $4 \ s$. In another $t \ s$,its mechanical energy becomes $12.5 \%$ of its initial mechanical energy. Then $t=$ (in $s$)

In a time of $2 \ s$,the amplitude of a damped oscillator becomes $\frac{1}{e}$ times its initial amplitude $A$. In the next two seconds,the amplitude of the oscillator is