Question

A bob attached to a string of length L = 1.25 m, initially found at the equilibrium

Answer 1

The maximum displacement angle of the bob is 13⁰.

The given parameters;

• Length of the pendulum, L = 1.25 m
• Initial velocity of the bob, v = 0.8 m/s

The maximum displacement of the bob is calculated by applying the principle of conservation of energy;

$P.E = K.E\\\\mgh = \frac{1}{2} mv^2\\\\h = \frac{v^2}{2g} \\\\h = \frac{0.8^2}{2\times 10} \\\\h = 0.032 \ m$

The maximum displacement angle is calculated as follows;

$cos \theta = \frac{L-h}{L} \\\\cos \theta = \frac{1.25 - 0.032}{1.25} \\\\\cos \theta = \frac{1.218}{1.25} \\\\cos \theta = 0.9744\\\\\theta = cos^{-1}(0.9744)\\\\\theta = 13\ ^0$

Thus, the maximum displacement angle of the bob is 13⁰.

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