Two particles are executing shm in a straight line

Asked by admin @ 17/08/2021 in Physics viewed by 275 People

Two particles are executing shm in a straight line with same amplitude a and time period t. At time t=0, one particle is at displacement x1=+a and the other at x2=a/2 and they are approaching towards each other. After what time they cross each other?

Answered by admin @ 17/08/2021

Let the equation of each particle in SHM is given by, $x=asin\omega t$

displacement of first particle , x = +a
e.g., angular displacement = π/2

displacement of 2nd particle, x = -a/2 [ negative sign indicates that 2nd particle approach the first particle ]
e.g., angular displacement = π/6

so, angular separation or phase difference = π/2 - π/6 = π/3

now, t = $\frac{\theta}{\omega}$

we know, $\omega$ = 2π/T

so, t = π/3/(2π/T) = T/6

hence, after T/6 time they cross each other .

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