# Find how far apart are the particles from each other

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1. Nov 16, 2014

### Angelique

1. The problem statement, all variables and given/known data
Two particles oscillate in simple harmonic motion with amplitude A, about the centre of a common straight line of length 2A. Each particle has a period of 3.3 s, and their phase constants differ by π/9 rad. (Assume the lagging particle starts at +A. Also assume that the +x-axis is to the right. Use any variable or symbol stated above as necessary.)
I want to find how far apart are the particles from each other (in terms of A) 0.50 s after the lagging particle leaves one end of the path?

2. Relevant equations
x(t) = Acos(wt + ϕ)
w= sqrt(k/m)
x(0) = Acos( ϕ)

3. The attempt at a solution
1. I found that w = 1.9
2. the phase constant for the lagging particle is 2pi or 0 since A=Acos(phase constant)
3. i used the equation for displacement and found that x = 0.58A for the lagging particle
4. the phase constant for the first particle is pi/9 for the second particle since we're told their phase constants differ by this much
Now my question is how do i find the displacement of the leading particle? Can i just use the same time (t value) as the lagging particle?
I already tried just using the same equation for the leading particle as i did for the lagging particle and only replacing ϕ with pi/9 instead of 0. But, i got the wrong answer
ie. lagging = x(0.5) = Acos(1.9(0.5) + 0) = 0.58m
x(0.5) = Acos(1.9(0.5) + pi/9) = 0.27
0.58-0.27= 0.31m

2. Nov 16, 2014

### Simon Bridge

... if particle 1 lags particle 2 by $\delta$ then $\phi_2-\phi_1=\cdots$ what?