A small ball is suspended by a thread of length l = 1 m at the point O on a wall, the thread making a small angle α = 2 ∘ with the vertical (Figure 5.112). The thread with the ball is deviated through

Question

A small ball is suspended by a thread of length $l = 1$ m at the point $O$ on a wall, the thread making a small angle $α = 2^{\circ}$ with the vertical (Figure 5.112). The thread with the ball is deviated through a small angle $β = 4^{\circ}$ and set free. The collision with the wall is perfectly elastic. Find the period of oscillation (take $g = π^{2}$ ):

TestHub · Accepted Answer

ω = g / l ​ = π , so the full period is 2 s for amplitude 4 ∘ . From 4 ∘ to the mean takes T /4 , then the mean to 2 ∘ takes sin ω t = 4 2 ​ , ω t = π /6 , i.e. T /12 . One way = T /3 , so the period is 2 T /3 = 3 4 ​ s.

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