Laplace problem 2. Try to solve this problem by Matlatb 2. Wheelchair (WC) can b

Question

Laplace problem 2. Try to solve this problem by Matlatb 2. Wheelchair (WC) can be modeled as one spring, mass and damper system as below. Find the trajectory for a mass spring damper system subject to an initial condition and an applied force using Matlab. At time t-0, this system is at position x -0, but with an initial velocity of 1 m/s. Beginning at this time, the force f(t) - e-3t, is applied. Find x(t) fort 2 0 and plot the trajectory for 10 seconds. (40 points) alt) alt) M(o f (t) Seat Cushion WC Frame S(o) alt) t),x MTS Rod SIT-BAR Force Platform F(o) Figure 1. (A) Wheel chair model and (B) simplified mass-spring-damper system Hint) 1) we can drive this to linear differential equations as below, 2) then taking the Laplace transform of both sides using matlab 3) partial fraction expansion and calculate coefficients using matlatb 4) Inverse Laplace Transform using matlab 5) plot time dependence trajectory for 10 second

Explanation / Answer

1.2. matlab code :

syms s t x
f=exp(-3*t);
F=laplace(f,t,s);
x1=s*x-0;
x2=s*x1-1;
sol=solve(x2+3*x1+2*x-F,x)
b=[1 4];
a=[1 6 11 6];
[r p k]=residue(b,a)
sol1=ilaplace(sol,s,t)
t=0:0.1:10;

y=(3*exp(-t))/2 - 2*exp(-2*t) + exp(-3*t)/2;

plot(t,y)

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