First slide

Simple hormonic motion

Question

A simple pendulum of length 1 m is allowed to oscillate with amplitude 2°. It collides elastically with a wall inclined at l° to the vertical. Its time period will be: (use g = $π^{2}$ )

Difficult

A

$\frac{2}{3} \sec$
B

$\frac{4}{3} \sec$
C

2 sec
D

none of these

Solution

Time period for half part:
$T = 2 π \sqrt{\frac{l}{g}} = 2 π \sqrt{\frac{l}{g}} = \frac{2 π}{π} = 2 \sec$
So 2° part will be covered in a time t = $\frac{T}{2}$ = 1 sec
For the left l° part:
$θ = θ_{0} \sin (ωt)$
1° = 2° sin( $\frac{2 π}{T} \times t$ ) $\Rightarrow \frac{1}{2} = \sin (\frac{2 π}{T} \times t)$
$\Rightarrow \frac{π}{6} = π \times t \Rightarrow t = \frac{1}{6} \sec$
Total time $\Rightarrow \frac{T}{2} + 2 t$

$\Rightarrow 1 + 2 \times \frac{1}{6} = 1 + \frac{1}{3} = \frac{4}{3} \sec$

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