The phase difference between displacement and acceleration of a particle in a simple harmonic motion is [2020]

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Solution

Q.
The phase difference between displacement and acceleration of a particle in a simple harmonic motion is [2020]

1 $π$ rad

2 $3 π / 2$ rad

3 $π / 2$ rad

4 zero

Ans.
(1)

Displacement of the particle, $y = a \sin ω t,$

$v = \frac{d y}{d t} = a ω$ $\cos$ $ω t$

Acceleration, $a = \frac{d v}{d t} = - a ω^{2} \sin$ $ω t$

So, phase difference between displacement and acceleration is $π$ .

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