- #1

Northbysouth

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## Homework Statement

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.

## Homework Equations

## 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:

```
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
```

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