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

If velocity is not large,then on which factor does the damping force on an oscillator in a medium depend?

$A$ 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 ..... $s$.

You are riding in an automobile of mass $3000\; kg$. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags $15\; cm$ when the entire automobile is placed on it. Also,the amplitude of oscillation decreases by $50 \%$ during one complete oscillation. Estimate the values of
$(a)$ the spring constant $k$ and
$(b)$ the damping constant $b$ for the spring and shock absorber system of one wheel,assuming that each wheel supports $750 \;kg$.

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.

$A$ steady force of $120 \ N$ is required to push a boat of mass $700 \ kg$ through water at a constant speed of $1 \ m/s$. If the boat is fastened by a spring and held at $2 \ m$ from the equilibrium position by a force of $450 \ N$,find the angular frequency of damped $SHM$ in $rad/s$.