# numerical integration to obtain response using convolution

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Shubham on 12 Mar 2021
Commented: Shubham on 15 Mar 2021
%% 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

Alan Moses on 15 Mar 2021
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!
Shubham on 15 Mar 2021
Very helpful now I am able to plot