FBD of Flexible and Rigid Body Coupling

[ThLiOp]

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!

 

[Dr.D]

The expression you wrote for Q(t) is positive when u(L,t)>y And the same for derivatives. Now look at your FBD; it shows positive Q to the let. There is your sign error.

 

[ThLiOp]

Thank you Dr.D, that makes sense now!