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

In damped oscillations,the damping force is directly proportional to the speed of the oscillator. If the amplitude becomes half of its initial value $A_0$ in $1 \, s$,then after $2 \, s$,the amplitude will be:

For the damped oscillator shown in the figure,the mass $m$ of the block is $200 \; g$,$k = 90 \; N m^{-1}$,and the damping constant $b$ is $40 \; g s^{-1}$. Calculate:
$(a)$ the period of oscillation,
$(b)$ the time taken for its amplitude of vibrations to drop to half of its initial value,and
$(c)$ the time taken for its mechanical energy to drop to half its initial value.

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

What is resonance? Give its example.

$Assertion :$ The amplitude of an oscillating pendulum decreases gradually with time.
$Reason :$ The frequency of the pendulum decreases with time.