# SImple Harmonic Oscillator under constant friction force

#### henryc09

1. The problem statement, all variables and given/known data
There is a mass attached to two springs on a table. Coefficients of static and sliding friction between the mass and table are equal with the value $$\mu$$.

The particle is released at time t=0 with a positive displacement x0 from equilibrium. Given that 2kx0 > $$\mu$$mg write down the equation of motion as long as it remains moving. Verify it's satisfied by x(t)=Acos(wt) + Bsin(wt) + C and find the constants A,B and C for the data given.

Find the time t1 and position x1 at which the particle next comes to rest.

2. Relevant equations

3. The attempt at a solution
I think I can do the verifying part, and am able to get B=0 after differentiating to find v which is 0 when t=0. Then A+C = x0 I think. The equation of motion is
ma=-2kx+ $$\mu$$mg i guess? Really don't know where to go from here. I worked out earlier in the absence of friction that the angular frequency w=sqrt(2k/m), is this still the same? Any ideas what to do next?

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