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**Problem:**

I am having a bit of problem with the signs on the force balance with the constraining force. The system is:

**Attempt:**

I drew the FBD with the constraining force for the lumped mass:

Then I tried to solve for the constraint force in terms of the spring and damper:

For the constraint force, Q(t), I end up getting:

Q(t) = k[u(L,t) - y] + c[(du/dt) - (dy/dt)]

The answer that the professor gives has the signs changed on the k and c terms. Where am I going wrong?

Thank you!