PhysicsThe angular amplitude of a simple pendulum is θ0. The maximum tension in the string is

The angular amplitude of a simple pendulum is $θ_{0}$ . The maximum tension in the string is

A
$mg (1 - θ_{0})$
B
$mg (1 + θ_{0})$
C
$mg (1 - θ_{0}^{2})$
D
$mg (1 + θ_{0}^{2})$

Solution:

$\begin{array}{l} A = {ℓθ}_{0}; ω^{2} = \frac{g}{ℓ} \\ T_{max} = mg + \frac{{mv}^{2}}{r} = mg + \frac{{mA}^{2} ω^{2}}{ℓ} \\ = mg + \frac{{mℓ}^{2} θ_{0}^{2}}{ℓ} \frac{g}{ℓ} = mg + {mgθ}_{0}^{2} = mg (1 + θ_{0}^{2}) \end{array}$

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