Displacement vs Time

Displacement in SHM: x(t) = A·cos(ωt + φ) (or equivalently sin form).

Maximum displacement is the AMPLITUDE A.

Crosses zero (equilibrium) twice per cycle. Reaches +A and −A once each per cycle.

Period T = 2π/ω; ωt + φ is the PHASE.

Position depends on initial conditions: x₀ and v₀ at t = 0.

If t = 0 is at extreme position: x(t) = A·cos(ωt).

If t = 0 is at equilibrium moving outward: x(t) = A·sin(ωt).

Both are valid SHM — phase shift relates them by π/2.