For any simple harmonic motion, the position, velocity, and acceleration can all be written as the same type of trigonometric function (sine or cosine) by correctly adding a relative phase factor.

(a) Show that an \(x\) component of the position function given by \(x(t)=\beta \cos (\omega t+\delta)\) is also a valid general solution for of the velocity and acceleration associated with this position function.

(c) Draw the reference circles for the \(x\) components of position, velocity, and acceleration, with the phasors correctly drawn for \(t=0\) and the amplitude clearly indicated.