I'm not sure I understand. From your equation, \phi = \epsilon = 0 (since \phi_0 = 0 clearly satisfies \ddot{\phi}=\dot{\phi}=0} ).
Is something wrong with the result I got above?
But then must not \ddot{\phi} = 0? If so, the second equation becomes Mg(L_0 + x)\phi = 0, which means \phi = 0; a bit excessive for a small angle approximation.
On the other hand, leaving \ddot{\phi} alone, x drops out completely from the second equation and (using x \ll L_0) I get...
I don't think inertia should affect the answer at all; inertia just tells you how fast something accelerates relative to applied force, and a constant motion situation involves no acceleration (linear or rotational).
The tension will always be equal no matter what the situation (assuming a...
Homework Statement
A spring of rest length L_0 (no tension) is connected to a support at one end and has a mass M attached at the other. Neglect the mass of the spring, the dimension of the mass M, and assume that the motion is confined to a vertical plane. Also, assume that the spring only...