Using ode45 to solve second order differential system

I am trying to solve a system m_1x'' + k_1x = 0; m_2x'' + k_2x = 0, with m_1,m_2,k_1,k_2 are some constants.

I read this post System of 2nd order DE, but I didn't follow how they do with their example, can someone show me how to do it? thanks

Answer 1

[Roger Stafford]

The same single function 'x' cannot in general satisfy two different differential equations, so you need to solve these equations separately.

It should be mentioned that you do not really need to use matlab's numerical ode functions on the particular equations you ask about. Their solution is well known in mathematics. If k/m is positive then x is of the form:

   x = A*cos(sqrt(k/m)*t)+B*sin(sqrt(k/m)*t)

If k/m is negative it is

   x = A*cosh(sqrt(-k/m)*t)+B*sinh(sqrt(-k/m)*t)

The constants A and B are determined by the two initial conditions which x must satisfy.