Question 1169739
y(t)=2sin(4πt) + 5cos(4πt)
In order to rewrite the equation in the form y(t)=A sin(wt+ Φ), we use the 
identity y(t) = AcosΦsin(wt) + AsinΦcos(wt) 
Thus c1 = AcosΦ = 2, c2 = AsinΦ = 5
If we divide the 1st by the 2nd, we have:
tanΦ = 5/2 = 2.5 -> Φ = 1.1903
Therefore, A = 5/sinΦ = 5.3852
So the equation of motion is y(t) = 5.3852*sin(wt + 1.1903)
The angular frequency, w = 4π
The period, T = 2π/w = 1/2, and the initial condition is y(0) = 5/sinΦ*sin(Φ) = 5.
One can also use the Pythagorean identity, as the problem suggests, to get the
amplitude: c1^2 + c2^2 = 25 + 4 = A^2(sin^2Φ + cos^2Φ) -> A = sqrt(29)