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Study of oscillations and how to solve in MATLAB

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Khang Ngo
Khang Ngo on 15 May 2021
Edited: Khang Ngo on 17 May 2021
The oscillation of any body due to elastic force can be described by the differential equation:
y''+b*y'+(w0^2)*y =F*cos(w*t)
In which, y is oscillation displacement, b is damped coefficient, w0 is angular frequency of free oscillation, w is angular frequency of stimulating force.
This project requires students to use Matlab to solve above equation to study harmonic oscillation (no damped, no stimulated force: b = F = 0), damped oscillation (b not equal 0, F = 0), stimulated oscilation (b not equal 0, F not equal 0).
Task
- Examine the command dsolve to solve differential equation in MATLAB symbolic calculation.
- Write Matlab program to solve and plot the graph depending on time (with initial conditions y(0) = 5; y’(0) = 0):
a) harmonic oscillation (w0 = 3; b = F = 0; t = 20s)
b) damped oscillation (w0 = 10; b = 0.01, 0.1, 1.0, 10.0 ; F = 0; t = 20s) % many values of b
c) stimulated oscilation (w0 = 10; b = 0.1 ; F = 10; w= 10.0, 5.0, 3.0, 0.0; t = 150s ) % many values of w
- Discuss about the obtained results.
Please somebody can help me deal with this problem, and explain me why we have this solution, I am a newbie and trying to improve my skill day by day.Thank you.

Answers (1)

Sulaymon Eshkabilov
Sulaymon Eshkabilov on 15 May 2021
This is a quite straight forward exercise. Follow these steps and run your different case scenarios:
syms y(t)
Dy = diff(y, t);
D2y = diff(Dy, t);
b = 0; F = 0; w0=3; % Harmonic MOTION. Free motion: no damping and no force applied
w=10;
SOL = dsolve(D2y==F*cos(w0*t)-b*Dy-y*w0^2, y(0)==0, Dy(0)==5);
fplot(SOL, [0, 20]), shg
%% Similarly simulate the other cases, as well. And compare your sim. results and discuss.
Good luck
  4 Comments
Khang Ngo
Khang Ngo on 17 May 2021
Does it right for the third case?
And why it has only 3 lines, I thought it has 4 instead.
Answer my question please. ^3^

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