1. The problem statement, all variables and given/known data The problem: The mass the m is placed on the rod with the bushing remaining stationary. The end of the rod deflects 2 cm. The bushing is then given a vertical motion y(t) = 0.4 sin (20t) cm. Determine the magnitude of the motion of the mass m (either relative to the bushing or to a fixed frame) for a stable solution. 2. Relevant equations Undamped harmonic motion. Structural dynamics. 3. The attempt at a solution I'm a little bit confused regarding how to deal with the fact that no force was given. Since they gave me the position of the bushing as a function of t I differentiated it twice to find the acceleration of the bushing: a(t)= - 160sin(20t) cm/s^2 so multiplying this by the mass should give me the force that is being applied on the bushing, correct? However, the rod is clearly not stiff since I am given a deflection, do I assume that the rod follows the motion of the bushing, i.e. that they have the same velocity at some arbitrary time t? If this is the case then I can find another initial condition and the problem becomes trivial. However, if I cannot assume this because of the elasticity of the rod then I am not given enough initial conditions and I get stuck. Am I thinking about this in the right way? edit: I assumed that the rod has negligible mass.