# A sliding mass

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Consider the mass m sliding horizontally under the influence of the applied force f and a friction force originating from a surrounding fluid that can be approximated by a linear friction element with coefficient b.

###A

Using the mobility analogy, determine the values of R and C in the circuit below (show RC circuit) in terms of the mechanical parameters, m, b, f, and u.

###B

The velocity of the mass is modeled by which variable:

###C

Consider the case where m = 1000 kg, and b = 100 N-s/m. Determine the steady-state velocity u(\infty) when the input is a constant force of 10 N.

###D

What is the numerical time constant of this system?

###E Assuming that the force now is a complex exponential drive of amplitude F_{in}. Determine analytically the transfer function between the velocity of the mass \widetilde{vel}_{out} and the input force amplitude.

`m`

, `b`

, `omega`

, and `j`

.

###F Does the relationship between the force and the velocity obey a low-pass, high-pass, band-pass, band-stop, or non-filtering relationship?