Question

Show that simple harmonic motion y(t) = C1 cos ωt + C2 sin ωt can be written as:

a. y(t) = A sin(ωt + ϕ0)

b. y(t) = A cos(ωt + ϕ1)

Answer 1

$A=\sqrt{C_1^2+C_2^2},$

$\phi_0=\arccos\frac{C_2}{\sqrt{C_1^2+C_2^2}},$

$\phi_1=-\arcsin\frac{C_2}{\sqrt{C_1^2+C_2^2}}.$