We've just begun studying oscillatory motion and recently derived the differential equation of motion for a helical using Hooke's law and Newton's second law of motion. The differential equation of motion for the helical spring is (dx/dt)^2 + (k/m)x = 0. In our lecture notes it says that the general solution to the above equation is x = Acos(ωt +θ), where θ is the phase constant. From this you can find the various equations for T, a and ω. Also, the notes go on to state that if θ = -pi/2 then Acos(ωt +θ) becomes Asin(ωt), which makes sense. However, in our text book it says that x = Asin(ωt +θ) is the general solution to the differential equation of motion and that is θ pi/2 then Asin(ωt +θ) becomes Acos(ωt), this also makes sense. So, I was just wondering is the general solution arbitrary or is there a mistake in either the notes or text? Thanks in advance.