(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Mass m moves along a line on a rough table and is attached on either side to a stretched spring (both have equal spring constants k). The coefficients of static and sliding friction between mass and the table are equal with value [tex]\mu[/tex]

(a) show in the abscence of friciton the particle executes SHM with angular frequency[tex]\omega[/tex] [tex]\sqrt{2k/m}[/tex]

(b) Now include the effect of friction. Suppose particle is released at time t=0 with positive displacement Xo from equilibrium. Describe initial motion when (i)2kXo> [tex]\mu[/tex]mg and (ii) when 2kXo =< [tex]\mu[/tex]mg

(c) For case (i) write down the equation of satisfied by the displacement x of the mass as long as it remains moving. Verify it is satisfied by a solution of the form:

x(t)=Acos(wt) + Bsin(wt) + C

and find the values of A, B and C for the data given.

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

2. Relevant equations

3. The attempt at a solution

Been a while since I last did S.H.M, but so far I have without friction total force on object will be -2kx which is equal to -mw^{2}x so i can show the first bit.

For part b I said that when 2kXo > [tex]\mu[/tex]mg it will oscillate with lower frequency and it's amplitude will gradually decrease, when 2kX0 =< [tex]\mu[/tex]mg it will remain stationary.

Part C is where I'm stuck. I think -mw^{2}x= - 2kx + [tex]\mu[/tex]mg but not sure how to show the solution and also how to go about working out the constants. Any point in the right direction would be appreciated.

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# Homework Help: Simple Harmonic Motion and friction

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