First slide

Applications of SHM

Question

A simple pendulum with length L and mass m of the bob is oscillating with an amplitude A. The maximum tension in the string is

Moderate

A

mg
B

mg $[1 + {(\frac{A}{L})}^{2}]$
C

mg ${[1 + (\frac{A}{2 L})]}^{2}$
D

mg ${[1 + (\frac{A}{L})]}^{2}$

Solution

$\begin{array}{l} T - m g \cos θ = \frac{m v^{2}}{L} \\ T is maximum when θ = 0, T_{max} - m g = \frac{m v_{max}^{2}}{L} \\ T_{max} = m g + \frac{m ω^{2} A^{2}}{L} \\ = m g + \frac{m g A^{2}}{L^{2}} (∵ ω^{2} = \frac{g}{L}) \\ T_{max} = m g [1 + \frac{A^{2}}{L^{2}}] \end{array}$

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