First slide

Applications of SHM

Question

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

Difficult

A

2/3 sec
B

4/3 sec
C

2 sec
D

none of these

Solution

Time period for half part:
$T = 2 π \sqrt{\frac{l}{g}} = 2 π \sqrt{\frac{1}{g}} = \frac{2 π}{π} = 2 \sec$
So 2^o part will be covered in a time $t = \frac{T}{2} = 1 \sec$
For the left 1^o part:
$\begin{array}{l} θ = θ_{0} \sin (ω t) \\ 1^{\circ} = 2^{\circ} \sin (\frac{2 π}{T} \times t) \Rightarrow \frac{1}{2} = \sin (\frac{2 π}{T} \times t) \\ \Rightarrow \frac{π}{6} = π \times t \Rightarrow t = 1 / 6 \sec \end{array}$
$\begin{array}{l} Total time \Rightarrow \frac{T}{2} + 2 t \\ \Rightarrow 1 + 2 \times \frac{1}{6} = 1 + \frac{1}{3} = \frac{4}{3} \sec \end{array}$

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