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1. A block of mass m is connected to a spring, the other end of which is fixed. There is also a viscous damping mechanism. The following observations have been made of this system:

i) If the block is pushed horizontally with a force equal to mg, the static compression of the spring is equal to h

ii) The viscous resistive force is equal to mg as the block moves with a speed u.

a) Write the differential equation governing horizontal oscillations of the mass in terms of m, g, h and u.

b) for the particular case of u = 3√gh, what is the angular frequency of the damped oscillations?

2. Homework Equations :

mx'' + λx' + kx = 0

3. The Attempt at a Solution :

F = mg = -kh (x = h)

F = mg = -λu for x' = u

At this point I'm somewhat lost and not sure what they're looking for. If the viscous force = mg at velocity u, how can you translate that into a differential equation that covers all velocities of the mass? Any help would be greatly appreciated