MA330-F16
Quiz 01
Q1 (Sec at 11am):
A cart (m = 1) is connected to an anchor by a parallel connection of a damper (c = 2) and a spring
(k = 3).
(a) Find the ODE for the position of the cart x using the balance of the forces. Justify your solution
via a fr
MA330-F16
Quiz 03
Q (Sec at 11am):
A system of ODEs for the vector of variables x (t)
1
x = 0
0
is given in the matrix form:
0
0
2 1 x.
1 2
h1i
One eigenvalue of the associated matrix is 1, with eigenvector 0 .
0
(a) Find the remaining two eigenvalues of
MA330-F16 Quiz 08
Q 11am:
(a) Explain the main mathematical difference between the PDE for the heat flow (heat equation) and the PDE
for the mechanical vibrations (wave equation) for the function u(t, x ) evolving in time and 1D space?
(b) The ODE F 00 (
MA330-F16 Quiz 06
If L[ f ] = F (s) then
L[ f (t)e at ] = F (s a)
L[ f 0 (t)] = sF (s) f (0)
Rt
L[ 0 f ( )d ] = F (s)/s
L[ f (t a)u(t a)] = F (s)e as ,
where u(t) is the unit step function at t = 0.
Unit step L[u(t)] = 1/s
Dirac L[(t)] = 1
Q 11am:
(
MA330-F16 Quiz 07
Q 11am:
Consider a PDE for the function u( x, y, t) evolving on the spatial domain D = [0, 1] [2, 4].
(a) Sketch the spatial domain D.
(b) Describe, in mathematical terms, the boundary D of the spatial domain D.
(c) Describe the differen
MA330-F16
Quiz 05
Q (Sec at 11am):
(a) Explain the relationship between the Fourier transform f( ) and the spectral density of the function f (t).
(b) Sketch graphs of any two functions f (t), g(t) such that | f( )| = | g ( )| for all , but whose phases o
MA330-F16
Quiz 04
Q (Sec at 11am):
Compute the Fourier coefficients a0 , an , bn of the periodic function given by the graph.
(a) Determine the fundamental period P the associated angular frequency of the function and
indicate it on the graph.
(b) Can you
MA330-F16
Quiz 02
Q (Sec at 11am):
The attached figure shows a city block with
flows of cars through inbound and outbound
one-way streets. The number of cars per hour is
written out next to every arrow. Traffic through
some streets (labeled by letters A,