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Hi, in a simple spring-mass system consisting of two identical springs, how would you treat the springs? Would Hookes equation be F = kx + kx?
Exactly - except - the spring constant of a spring varies inversely with its length! This means that placing two identical springs in series you now have a single spring with half the effective spring constant.HallsofIvy said:Tides point is that if you attach two identical springs end to end, effectively you still have just one spring (of twice the length) still with spring constant k.
If you have two identical springs side by side (and both attached to the mass) then the act identically and then you can add them.
What if the springs aren't hanging but are placed horizontally?robphy said:Let us hang a mass M from spring 1: so, k_{1} x_{1}=Mg.
Let us hang a mass M from spring 2: so, k_{2} x_{2}=Mg.
If we hang the mass M from the springs arranged in series,
we have an effective spring with spring constant K and displacement X=x_{1}+x_{2}.
Since KX=Mg, we find
x_{1} = KX/k_{1} and
x_{2} = KX/k_{2}.