A particle moves with simple harmonic motion in a straight line. In first τ s, after starting from rest it travels a distance a, and in next τ s it travels 2a, in same direction, then

Engineering

Physics

Basics of Simple Harmonic Motion

Question

amplitude of motion is 4a

amplitude of motion is 3a

time period of oscillations is 8τ

time period of oscillations is 6τ

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R – cos $θ$ = a

R – R cos 2 $θ$ = 3a

$\frac{1 - cosθ}{1 - \cos 2 θ} = \frac{1}{3}$

$\frac{1 - cosθ}{2 \sin^{2} θ} = \frac{1}{3}$

3 – 3 cos $θ$ = 2 – 2 cos² $θ$

2 cos² $θ$ – 3 cos $θ$ + 1 = 0 $∴$ $θ$ = 60º

2cos² $θ$ – 2cos $θ$ – cos $θ$ + 1 = 0

2cos $θ$ (cos $θ$ – 1) – 1

$θ$ = 60º