Damped spring (no driving force)

[mathman44]

Homework Statement

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 about the system:

1) if the block is pushed horizontally with force = mg, the static compression in the spring is "h"

2) the viscous resistive force = mg if the block moves with a known speed "u"

Questions:
a) Write the differential equation governing the horizontal oscillation of this mass in terms of m,g,h,u.
b) if u is known to be = $$3\sqrt(gh)$$ what is the angular frequency of the damped oscillation?

--solved--

thanks

 

[Filip Larsen]

Note, that the angular frequency of a damped and undamped oscillation are not exactly the same, although they are related.