Which of the following quantities does $NOT$ change due to the damping of oscillations?

$A$ simple pendulum oscillates in air with time period $T$ and amplitude $A$. As the time passes,

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.

$A$ particle of mass $m$ is attached to a spring (of spring constant $k$) and has a natural angular frequency $\omega_0$. An external force $F(t)$ proportional to $\cos \omega t$ (where $\omega \neq \omega_0$) is applied to the oscillator. The displacement of the oscillator will be proportional to:

When two violin wires with different fundamental frequencies are vibrated to play some music,can they produce resonance?

When an external force with angular frequency $\omega_d$ acts on a system of natural angular frequency $\omega$,the system oscillates with angular frequency $\omega_d$. The condition for the amplitude of oscillations to be maximum is