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## Homework Statement

This is an example of an Undamped Forced Oscillation where the phenomenon of Pure Resonance Occurs.

Find the solution of the initial value problem:

x'' + 4 x = 8 sin(2 t) , x(0)=x'(0)=0

## Homework Equations

## The Attempt at a Solution

in class we were given the equation:

x''+(k/m)x=(F0/m)cos(ѡt)

and,

x_p= [(F0/m)/(ѡ0^2-ѡ^2)]cos(ѡt)

where ѡ0=sqrt(k/m)

However, in this equation ѡ=2 and ѡ0=sqrt(4)=2

so, the equation to find x_p fails... since ѡ0^2-ѡ^2 =0

I feel like I am just missing something here... anyone want to help me out?