# Matlab: Numerically Integrate and Plot Response of Underdamped System

1. Mar 16, 2014

### Northbysouth

1. The problem statement, all variables and given/known data
Numerically integrate and plot the response of an underdamped system determined by m= 100 kg,
k= 20,000 N/m, and c = 200 kg/s, subject to the initial conditions of x0 = 0.01 m and v0 = 0.1 m/s, and the applied force F(t)=150cos(5t). Then plot the exact response.

2. Relevant equations

3. The attempt at a solution

I've been trying to use matlab to solve this question, but I'm having a little trouble. I started by defining the variables and the time durations. I was attempting to use the state space form to solve the problem, hence I defined matrices A, B, C and D

Code (Text):

m=100; k=20000; c=200; x0=0.01; v0=0.1; f0=150; w=5;
F0=f0/m;
t=[0:0.1:5];

A=[0 1; -k/m -c/m];
B=[0; 1];

C=[0 1;1 0];

D=[];

sys=ss(A,B,C,D);

u=F0*cos(w*t);

lsim(sys,u,t,x0,v0)

[code]

When I run the code I get:

Error using DynamicSystem/lsim (line 98)
Invalid syntax for time or frequency response command. See command help for more
information.

Error in ME_3504_chapter2_80a (line 17)
lsim(sys,u,t,x0,v0)

I don't understand what the problem is. I can see it's to do with lsim, but I'm not sure how to fix it. I suspect that it may have something to do with the initial conditions x0 and v0.

Any advice would be greatly appreciated. Thank you

Last edited: Mar 16, 2014
2. Mar 16, 2014

### SteamKing

Staff Emeritus
If you have written Matlab routines to solve your problem, please share them so that we can make sense of the errors you have gotten. Don't forget to use
Code (Text):
tags for the source.

3. Mar 16, 2014