How Is the Amplitude Calculated in a Damped Spring-Mass System?

[mcafej]

Homework Statement

A mass of 4 kg is stretches a spring by 1 m. An external force of cos (!t)
N acts on the mass. Assume that the damping constant is nonzero and gravity is 10 ms^-2.
Consider a spring mass system described by the following IVP.

u''+yu'+u = cos(wt)
u(0) = 0
u'(0) = 0

1) Find the amplitude of the spring mass system in terms of w and y.

The Attempt at a Solution

The solution says

R² = 1/((1-w²)²+w²y²)

But how is that the solution, I can't find how to compute the amplitude in my textbook, it just says R²=A²+B².

 

[Simon Bridge]

It comes from the general solution to the differential equation.