Having trouble doing this differential equation ...

[Sicar]

First time taking this course, concept is lost on me. Problem seems simple enough.

x" + 4x = 0

x(0) = 1 x(0)'=0 given initial values ..


I just don't know where to start with it. It needs to be done without using LaPlace transforms?

 

[_Eduardo_]

x" + 4x = 0

x(0) = 1 x(0)'=0 given initial values ..


You must know some theory of differential equations:
https://en.wikipedia.org/wiki/Linear_differential_equation

Then, the characteristic equation is z^2+4 = 0 --> z = +/- 2j (j imaginary unit)

The general solution is:
x(t) = A*exp(j 2t) + B*exp(-j 2t) = C*cos(2t) + D*sin(2t)

But x(0) = 1 and x(0)'=0 --> C=1, D=0 --> x(t) = cos(2t)

 

[Sicar]

Thanks man. Very good explanation!