Mechanical Engineering 521
Mechanical Vibrations
Problem 1
A mass-spring-damper system is subjected to the loading shown below.
Question 1: Express the load, $f(t)$, as a Fourier series. Be sure to explicitly calculate all of the
coefficients, $a_i$ and $b_i$.
Question 2: Make a plot similar to what I handed out in class for the square wave problem. Show
the Fourier series with three terms retained. Next, show the Fourier series with 10 terms retained.
Finally, show the Fourier series with 3000 terms retained. Comment on how well the series represents
the function shown. Suggestion: you'll need to use Matlab (or similar).
Question 3: Assume that the system is governed by the differential equation
$m\ddot{x} + c\dot{x} + kx = F(t)$,
with $F(t)$ given by the above waveform (which can be represented by the infinite Fourier Series).
Determine the dynamic response of the system $x(t)$.
Due 09/26/17
Assignment 4
