First slide

Simple harmonic motion

Question

The displacement of a particle is given by $y = a \sin (2 π t + ϕ)$ then

Easy

A

The motion is oscillatory but not simple harmonic motion
B

The motion is simple harmonic with amplitude a
C

The motion is simple periodic but not simple harmonic motion
D

The motion is simple harmonic whose frequency is $2 π$ .

Solution

The equation $y = a \sin (2 π t + ϕ)$ represents simple harmonic motion which takes the form $y = A \sin (ω t + ϕ)$ . On comparing with standard equation we get amplitude A = a, angular Frequency $ω = 2 π$ and phase $ϕ$

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