First slide

Periodic Motion

Question

Angular amplitude of a simple pendulum is $θ_{0}$ . Maximum tension in the string for small $θ_{0}$ will be:

Moderate

A

$mg (1 - \cos θ_{0})$
B

$mg (1 + θ_{0})$
C

$mg (1 - θ_{0}^{2})$
D

$mg (1 + θ_{0}^{2})$

Solution

$T - mg = \frac{{mv}^{2}}{l} But v^{2} = 2 gl (1 - \cos θ_{0}) So T = mg + 2 mg (1 - \cos θ_{0}) T = mg + 2 mg (2 \sin^{2} \frac{θ_{0}}{2}) T \approx mg + 4 mg {(\frac{θ_{0}}{2})}^{2} T \approx mg (1 + θ_{0}^{2})$

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