Amplitude of S.H.M.

Consider a particle P performing linear S.H.M. along a straight-line path MN, with O marking the centre of MN -- the mean (equilibrium) position of the particle (Fig. 5.2). From the general displacement expression $x = A\sin(\omega t+\phi)$ (Eq. 5.12), the particle's displacement reaches its greatest possible magnitude exactly when $\sin(\omega t+\phi) = \pm 1$, i.e. when $x = \pm A$. This maximum possible displacement, A, is called the amplitude of the S.H.M.

Formally: the amplitude of a particle performing S.H.M. is the maximum displacement of the particle from its mean position. Geometrically, in Fig. 5.2, the amplitude A is simply the distance OM (or, equivalently, ON) -- the half-length of the full oscillation path MN. It is a positive quantity, fixed for a given oscillation (it does not change from one cycle to the next unless energy is added to or removed from the system, as happens under damping, section 5.14), and it sets the overall " …