numerical integration to obtain response using convolution

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Shubham
Shubham 2021-3-12
评论： Shubham 2021-3-15
%% Question - I have to integrate this expression symbollically such that the final answer is a function of ta
%% because I have to plot response v\s ta , but I am getting a symbollic expression
syms ta tau
m = 2;
wn=707.10678;
wd = 707.10236;
z=0.003535;
F = -8.492 -18.92 *cos(ta*4) + -7.036e-14 *sin(ta*4) + -11.03*cos(2*ta*4) + -8.148e-13*sin(2*ta*4)+-9.687 *cos(3*ta*4) + -7.713e-13 *sin(3*ta*4) + -9.277*cos(4*ta*4) + -6.027e-13*sin(4*ta*4)+-4.587 *cos(5*ta*4) + 5.084*sin(5*ta*4);
response = 1/(m*wd)int(F*exp(-z*wn(ta-tau))sin(wd(ta-tau)),tau,0,ta);
pretty(response)
subs(response,3.5) %% Tried finding the value at ta = 3.5
%% plot response at some 4-5 valuse of ta

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Alan Moses
Alan Moses 2021-3-15
The code attached produces an error due to missing multiplication operators. You may replace the line 10 of your code where the 'response' variable is calculated with the below line:
response = 1/(m*wd)*int(F*exp(-z*wn*(ta-tau))*sin(wd*(ta-tau)),tau,0,ta);
You may also check out the vpa function that substitutes the value of 3.5 to the ‘response’ symbolic expression. You may use the following line of code:
vpa(subs(response,3.5))
Hope this helps!

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