A ball is suspended by a thread of length λ at a point O on a vertical wall, making a small angle α with the vertical. It is displaced through a small angle β (β > α) and released. Assuming perfectly elastic collision with the wall, find the period of oscillation.

Question

G1 Physics · Accepted Answer

Between impacts the bob follows small-angle pendulum SHM with ω=√(g/λ). The phase needed to move between angular positions β and α is obtained from cosφ=α/β. Including the symmetric return and the perfectly elastic velocity reversal at the wall gives T=2√(λ/g)[π/2+sin⁻¹(α/β)]. Correct answer: A.

A ball is suspended by a thread of length λ at a point O on a vertical wall, making a small angle α with the vertical. It is displaced through a small angle β (β &gt; α) and released. Assuming perfectly elastic collision with the wall, find the period of oscillation.

A ball is suspended by a thread of length λ at a point O on a vertical wall, making a small angle α with the vertical. It is displaced through a small angle β (β > α) and released. Assuming perfectly elastic collision with the wall, find the period of oscillation.