First slide

Simple hormonic motion

Question

Two particles are executing simple harmonic motion. At an instant of time t, their displacements a
$y_{1} = A \cos (ωt) and y_{2} = A \sin (ωt)$ Then, the phase difference between y₁ and y₂ is

Easy

A

$120 °$
B

$90 °$
C

$180 °$
D

zero

Solution

$y_{1} = A \cos ωt = A \sin (ωt + \frac{π}{2})$
$y_{2} = A \sin ωt$
$∴ Δϕ = ωt + \frac{π}{2} - ωt = \frac{π}{2} = 90 °$

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