Hi. I am having issues with having my matlab get past the ifourier part of my code. It just continually runs and is stuck at that part. The bold is where my computer is stuck.

m = 10; % kg

k = 15; % N/m

b = 8;

syms x(t)

Dx = diff(x,t);

h_eqn = m*diff(x,t,2) + b*diff(x,t,1) + k*x;

Initial_conds = [x(0)==25 , Dx(0)==5];

h_solve = dsolve(h_eqn,Initial_conds);

t = linspace(0,10,1000);

ht = eval(h_solve);

syms t w

f_sym = exp(-2*t).*heaviside(t-3);

imp_sym= ht.*heaviside(t);

four_f_t = fourier(f_sym,t,w);

four_h_t = fourier(imp_sym,t,w);

X_w = four_h_t*four_f_t;

x_t = ifourier(X_w,w,t);

xt_vector = eval(x_t);

t = linspace(0,10,1000);

plot(t, xt_vector,'LineWidth',2)

[Paul]

Hi Justin,

If you don't mind me asking, what is the intent of this code? It first finds the response of the mass-spring-damper to particular initial conditions. That result is called 'imp_sym,' which sounds like the name of an impulse response, the FT of which is then muliptiled with the FT of f(t), which sounds like a force input. That multiplication would make sense if imp_sym actually is the impulse response, but it isn't. Based on just an educated guess (which could be wrong), something doesn't seem right, so I thought I'd ask.

[Justin Bryant]

Fourier Transforms: Declare t and ω symbolically. Redefine f(t) from part B as a symbolic

equation. Use the built in function fourier() to find the Fourier transform, F(ω), of f(t). Use the built

in function fourier() to find the Fourier transform, H(ω), of h(t).

(Hint: Use the symbolic h(t) equation that you got as your output from dsolve() in part A multiplied

by the unit step function as your input to fourier().)

In the Fourier domain, calculate X(ω) as a symbolic equation. Use the built in function ifourier() to

perform the inverse Fourier transform to get x(t) as a symbolic equation. Redefine your time vector

and use eval() to calculate x(t). Plot x(t) vs. t in the figure space indicated in the diagram above and

title the plot “Fourier Transform”

[Paul]

Was dsolve() in part A used to solve an initial condition problem? If so, then all is fine, even though that doesn't make sense to me. But it only needs to make sense to you.

Answer 1

[Star Strider]

It seems to work here —

m = 10;  % kg
k = 15;  % N/m
b = 8;   
syms x(t)
Dx = diff(x,t);
h_eqn = m*diff(x,t,2) + b*diff(x,t,1) + k*x;
Initial_conds = [x(0)==25 , Dx(0)==5];
h_solve = dsolve(h_eqn,Initial_conds)

h_solve = 

t = linspace(0,10,1000);
% ht = eval(h_solve);
ht = h_solve;
syms t w
f_sym = exp(-2*t).*heaviside(t-3);
imp_sym= ht.*heaviside(t);
four_f_t = fourier(f_sym,t,w);
four_h_t = fourier(imp_sym,t,w);
X_w = four_h_t*four_f_t;
x_t = ifourier(X_w,w,t)                    % 

x_t = 

% xt_vector = eval(x_t);
% t = linspace(0,10,1000);
% plot(t, xt_vector,'LineWidth',2)

figure
fplot(x_t, [0 10])
grid
xlabel('t')
ylabel('x\_t')

I eliminated the eval calls. (Perhaps that could be the problem?) I also replaced the plot call with the fplot call.

.

[Justin Bryant]

It worked. Thank you so much! I don't know why I was having a hard time.

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

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