Advanced Higher Physics

Definition of SHM in terms of the restoring force and acceleration proportional to, and in the opposite direction to, the displacement from the rest position.

Use of calculus methods to show that expressions in the form of y=\mathrm{A\; sin\; \omega t} and y=\mathrm{A\; cos\; \omega t} are consistent with the definition of SHM ( a={\mathrm{-\omega }}^{2}y )

Derivation of the relationship v=\pm \omega \sqrt{A^2-y^2} and E_k=\frac{1}{2}{\mathrm{m\omega }}^2{\mathrm{(A}}^2-y^2)

Use of appropriate relationships to solve problems involving the displacement, velocity, acceleration, force, mass, spring constant k, angular frequency, period, and energy of an object executing SHM.

F=\mathrm{-ky}

\omega =\mathrm{2\pi f}=\frac{\mathrm{2\pi }}{T}

a=\frac{d^{2}y}{{\mathrm{dt}}^2}=-{\omega }^{2}y

y=\mathrm{A\; cos\; \omega t}=\mathrm{A\; sin\; \omega t}

v=\mathrm{\pm \omega }\sqrt{A^2-y^2}

E_k=\frac{1}{2}{\mathrm{m\omega }}^2{\mathrm{(A}}^2-y^2)

E_p=\frac{1}{2}{\mathrm{m\omega }}^2{y}^2

Knowledge of the effects of damping in SHM to include underdamping, critical damping and overdamping.