Two particles are executing S.H.M in a straight line At t=0 one particle is at x1 = +A and the other at x2 = -A/2, and they are approaching towards each other. After what time they cross each other (A,T are same)
Question
Two particles are executing S.H.M in a straight line At t=0 one particle is at x1 = +A and the other at x2 = -A/2, and they are approaching towards each other. After what time they cross each other (A,T are same)
Solution
The problem involves two particles executing Simple Harmonic Motion (S.H.M) in a straight line.
The equations of motion for the two particles can be written as:
x1 = A cos(wt) for the first particle and x2 = -A/2 cos(wt) for the second particle.
The particles cross each other when x1 = x2.
Setting the two equations equal to each other gives:
A cos(wt) = -A/2 cos(wt)
This simplifies to:
2 cos(wt) = -1
The solution to this equation is:
wt = 2π/3 or 4π/3
Since the period T = 2π/w, the time at which the particles cross each other is:
t = T/3 or 2T/3
So, the particles will cross each other at T/3 or 2T/3.
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