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Oscillations

Question

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The angular amplitude of simple pendulum is θ_o. The maximum tension in its string will be

mg ( 1 $-$ θ₀ )

mg ( 1 + cosθ₀)

mg ( 1 $-$ cos $θ_{0}^{2}$ )

mg ( 1 + cos $θ_{0}^{2}$ )

Solution

D.

mg ( 1 + cos $θ_{0}^{2}$ )

Maximum tension in the string is

T_max = mg + $\frac{m v^{2}}{l}$

= mg + $\frac{2 mg l}{l}$ ( 1 - cosθ₀ )

= mg + 2mg $(1 - 1 + \frac{θ_{0}^{2}}{2})$ ( since θ₀ is small )

T_max = mg ( 1 + θ₀)

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