Suppose there is a square plate, of side a and mass M, whose
corners are supported by massless springs, with spring constants K, K, K, and k <= K
(the faulty one). The springs are confined so that they stretch and compress vertically,
with unperturbed length L. The density of the plate is uniform.
(it's a car so the square plate is the chassis and the springs are the suspension)
Explain why the system requires three generalised coordinates to be described
The Attempt at a Solution
I'm just really having a hard time visualizing the actual motion of the plate on the springs.
I know there should be a generalized coordinate associated with the displacement of the spring, for each spring.. but I can't make the connection and reduce the number to 3 generalized coordinates, as specified.
I'm thinking that the springs on opposite corners are somehow related..i.e as one goes up the other goes down, but what happens to the 2 other springs in this case?
thanks in advance.