Displacement vs Time
Live x(t) graph with adjustable A, ω, φ.
Key Notes
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.
Formulas
General displacement
Most general form; constants A and φ from initial conditions.
Alternative sine form
ψ = φ + π/2. Equivalent.
Amplitude from initial conditions
Determined by initial position and velocity.
Initial phase
Watch quadrant signs when computing.
Important Points
x oscillates between +A and −A symmetrically about equilibrium.
Time-average of x over a full period is zero. RMS = A/√2.
Initial conditions (x₀, v₀) determine A and φ — period and ω are set by the SYSTEM.
Phase tells you WHERE in the cycle you are — most useful when comparing two oscillations.
Plot of x(t) is a sinusoid — characteristic 'wavy' line.
Common pitfall: confusing displacement (vector with sign) with distance traveled (always positive, increases monotonically).
Displacement vs Time notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.