Order Linear with a Forcing Function
Order Linear with a Forcing Function
The second order linear ODE
arises in many applications. Two of the more obvious are LRC circuits and
harmonic oscillators. The purpose of this lab is to illustrate the effect of
forcing functions on different linear ODE's.
The first three are more prevalent in applications:
1.
For this one we will make 4 different graphs. Using
and
make a graph for each value of
0.5, 1.2, 1.4, 2.0. One on these will illustrate beats and another
resonance while the other two are noise, Try to decide as to which is which.
Run the t scales far enough to determine what is happening in each case.
2.
For this one we will change the initial condition,
,
values and graph all on the same graph. Let
while x'(0)=0. What seems to be happening now?
3.
Now we change the forcing function and graph all on the same graph. For
simplicity and for clarity as to whats happening we are going to let
be the constant functions
,
For 4., 5., 6. make one graph
each showing the three equations on the same field. In each case use
and try to decide what effect the forcing function has on the graphs.
4.
and
and
5.
and
and
6.
and
and
Report your findings.
This document created by Scientific Notebook 4.1.