MATLAB: How to solve these differential equations set

Question

Hi, I tried solving a system with masses and springs, using the Lagrangian approach. I got the below equations of motion. fx1 =M1*D(D(y1))(t) – F + K*(s0 + y1 – y2 – r*sin(ph)) fx2 = F + M2*D(D(y2))(t) – K*(s0 + y1 – y2 – r*sin(ph)) fx3 =I*D(D(ph))(t) + F*r*cos(ph) – K*r*cos(ph)*(s0 + y1 – y2 – r*sin(ph))

Now I want get the equations of solutions for the variables y1, y2 and phi. I tried solving it using the dsolve command sol { dsolve(eqns) }.

I get solutions for the variables as follows ans = C15 + C12*t – (F*t^2)/(2*M2) + (K*s0*t^2)/(2*M2) + (K*t^2*y1)/(2*M2) – (K*t^2*y2)/(2*M2) – (K*r*t^2*sin(ph))/(2*M2)

ans = C16 + C11*t + (F*t^2)/(2*M1) – (K*s0*t^2)/(2*M1) – (K*t^2*y1)/(2*M1) + (K*t^2*y2)/(2*M1) + (K*r*t^2*sin(ph))/(2*M1)

ans = (K*r*s0*t^2*cos(ph))/(2*I) – (F*r*t^2*cos(ph))/(2*I) – (K*r^2*t^2*sin(2*ph))/(4*I) + (K*r*t^2*y1*cos(ph))/(2*I) – (K*r*t^2*y2*cos(ph))/(2*I)

My question is, I was expecting some exp(k/m) form of expression (general solution of (y" + y = 0), i.e e^x). How do I know if the solutions are correct.

Answer 1

you can try the ode function. Use ode45 to solve the differential equations and then plot your solution using plot function. For more info, take a look at the matlab page: https://in.mathworks.com/help/matlab/ref/ode45.html for examples.