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jsmith613
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Looking at the three diagrams we can see that there are three possible situations
(a) mass is to the right of eqm
(b) mass is at eqm
(c) mass is to the left of eqm
(eqm = equilibrium)
Lets look at position (a)
If we consider the tension in both springs:
the tension in the spring on the left has increased by k1x
the tension in the spring on the right has decreased by k2x
So the overall restoring force SHOULD BE k1x - k2x
(the spring on the left is trying to pull it back to the left and the spring on the right is trying to pull it the right hence the forces act in opposite directions)
BUT according to my book the overall restoring force is k1x + k2x...how?
Any help is greatly appreciated
exact quote:
Book
Consider the mass at some point during motion. Let its displacement from eqm be x at that point. One of the two springs has been extended by x and the other has been shortened by x. So compared with eqm one spring has extra tension k1x and the other string has its tension reduced by k2x.
The spring constants for the individual springs are k1 and k2.
The extra tension from one spring combines with the reduced tension from the other to give a restoring force of k1x + k2x.
The restoring force can be written as: F = -kx
where k = k1 + k2
The - sign indicates it acts towards eqm