First slide

Simple hormonic motion

Question

The phase difference between two particles executing SHM of the same amplitudes and frequency along same straight line while passing one another when going in opposite directions with equal displacement from their respective stating point is $\frac{2 π}{3}$ . If the phase of one particle is $\frac{π}{6}$ , find the displacement at this instant, if amplitude is A.

Difficult

A

$\frac{A}{3}$
B

$\frac{2 A}{3}$
C

$\frac{3 A}{4}$
D

$\frac{A}{2}$

Solution

Phase difference $δ = \frac{2 π}{3} = δ_{2} - δ_{1} = δ_{2}$
= $δ_{2} - \frac{π}{6} \Rightarrow δ_{2} = \frac{5 π}{6}; \sin δ_{1} = \sin δ_{2} = \frac{1}{2}$
Displacement is measured from starting point (t = 0)
So, $x = A \sin (ωt + δ_{1}); A \sin (0 + \frac{π}{6}) = \frac{A}{2}$

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