# Mechanics question help please

A particle of mass m is constrained to move vertically within a rigid box; a vertical spring and a damper arranged in parallel are attached between the top of the box, A, and the particle, P, while the other damper is attached between the particle and the bottom of the box, B. The box is placed on the machine whose motion is to measured. The distance of the particle P from the floor is x, and the displacement of the bottom of the box, B, from the floor is y. H is the height of the box- the distance AB. I vertically upwards
a)i) The natural length of the spring is l_o. what is spring length and the extension? and hence the spring force?
ii)What is the length of damper PA? The rate of change of length of this damper and hence the force of this damper.
Do the same for damper PB
b) write down a differential equation of motion satisfied by the particle
c) find the equilibrium position of the particle in terms of the parameters of systems,when a machine is static and y=1.25 The parameters are: m=0.2kg; k=2000N m^-1; r_1=20N sm^-1; r_2=50N sm^-1; l_o=0.2m; H=0.3m
d) Determine whether this system is weakly, strongly or critically dampened
Asked Mar 26, 2013

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Answered Jun 03, 2015

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Answered Jun 03, 2015

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