To understand how the two standard ways to write the general solution to a harmonic oscillator are related. there are two common forms for the general solution for the position of a harmonic oscillator as a function of time t: x(t)=acos(ωt+ϕ) and x(t)=ccos(ωt)+ssin(ωt). either of these equations is a general solution of a second-order differential equation (f⃗ =ma⃗ ); hence both must have at least two--arbitrary constants--parameters that can be adjusted to fit the solution to the particular motion at hand. (some texts refer to these arbitrary constants as boundary values.)