Two Spring System: Steady State Motion

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Homework Statement


Consider a system consisting of two springs suspended from the ceiling. The first has a spring constant k-1, the second k-2. They are connected by a mass m and the second spring also has a mass m connected at the bottom. A periodic force is applied to the upper mass. What is the steady state motion for each mass?



Homework Equations


Fcoswt
x1 = Acos wt
x2 = Bcos wt


The Attempt at a Solution

 
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Welcome to PF!

Hi mwkfun! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
 
I tried two different ways...I attempted to turn the system into an electrical circuit equivalent and I tried with free body diagrams and the following equations:
mX=mg + k1x1 + k2x2 - Fcoswt
mX=mg + Fcoswt - k1x1 - k2x2

(For these two eqns. the X means X double dot indicating acceleration)

mX2 = mg + k2x2 - Fcoswt
mX2 = mg + Fcoswt - k2x2

(again, X2 indicates x double dot...I don't know how to type it the correct way)
I think I should be solving for x1 and x2, but I am not sure if I have the correct equations. The eqns. reflect the free body diagrams I have drawn. Thanks for any help you can give.
 
I am also wondering whether I should use the x1= Acoswt and x2 = Bcoswt as a substitutions or if they are specific solutions to the differential eqns.
 
mwkfun said:
… I tried with free body diagrams and the following equations:
mX=mg + k1x1 + k2x2 - Fcoswt
mX=mg + Fcoswt - k1x1 - k2x2

(For these two eqns. the X means X double dot indicating acceleration)

mX2 = mg + k2x2 - Fcoswt
mX2 = mg + Fcoswt - k2x2

Hi mwkfun! :smile:

(on this forum, it's best to use dashes instead of dots: X1'' :wink:)

I don't understand why you've put each of these equations in pairs :confused:

Anyway, you need to take into account that the displacement of the lower mass is not the same as the displacement of the lower spring … it's the displacement of the lower spring minus the displacement of the upper spring :smile:
 
Thanks so much for your help. I think I got it!
 

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