First slide

Simple hormonic motion

Question

Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is

Moderate

A

zero
B

$\frac{2 π}{3}$
C

$π$
D

$\frac{π}{6}$

Solution

Equation of SHM is given by x = A sin ( $ωt+δ$ )
$(ωt = δ) is called phase .$
when x = $\frac{A}{2}, then$
$\sin (ωt + δ) = \frac{1}{2} \Rightarrow ωt + δ = \frac{π}{6}$
or $φ_{1} = \frac{π}{6}$
For second particle, $ϕ_{2} = π - \frac{π}{6} = \frac{5 π}{6}$
$∴$ $ϕ_{2} - ϕ_{1}$
= $\frac{4 π}{6} = \frac{2 π}{3}$

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