Home / Exercises 10 / A sliding mass

A sliding mass

The questions below are due on Wednesday November 20, 2019; 11:59:00 PM.
 
You are not logged in.

If you are a current student, please Log In for full access to the web site.
Note that this link will take you to an external site (https://shimmer.csail.mit.edu) to authenticate, and then you will be redirected back to this page.

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.

R=

C=

###B

The velocity of the mass is modeled by which variable:

Choose the correct 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.

u(\infty) [m/s] =

###D

What is the numerical time constant of this system?

\tau [s] =

###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.

Enter in terms of m, b, omega, and j.

\frac{\widetilde{vel}_{out}}{F_{in}}=

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

Choose the correct response: