Question #43577

A coherent point light source $S$ emitting light of wavelength $\lambda$ (in $\text{m}$) is attached to the bob of a simple pendulum. The pendulum consists of a small spherical bob of mass $m$ (in $\text{kg}$) and radius $a$ (in $\text{m}$), suspended by a massless string of length $L$ (in $\text{m}$). The source $S$ is positioned at a distance $D'$ (in $\text{m}$) behind a plane containing two narrow slits separated by a distance $d$ (in $\text{m}$). The equilibrium position of the pendulum lies exactly on the central axis of the double-slit system. The pendulum oscillates in a vertical plane parallel to the slit plane, within a medium of viscosity $\eta$ (in $\text{Pa}\cdot\text{s}$). At $t=0$, the pendulum is released from a small initial angular displacement $\theta_0$ (in $\text{rad}$). An interference pattern is observed on a screen placed at a distance $D$ (in $\text{m}$) from the slits. (Assume the initial amplitude of the central maximum is strictly greater than one fringe width). Assuming small angle approximations and underdamped oscillations, what is the time $t$ (in $\text{s}$) after which the amplitude of oscillation of the central maximum on the screen reduces to exactly one fringe width?