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SHM displacement
Beginner
Sinusoidal displacement in time.
x = A cos(ωt+φ)x = A cos(ωt + φ), with φ fixed by the initial conditions. It's the projection of uniform circular motion.
x₀ = A at t = 0 gives φ = 0.
Be careful with sine or cosine form; they differ by phase π/2.
In more detail
The displacement in SHM is x(t) = A cos(ωt + φ), a sinusoidal function of time. The amplitude A sets the maximum displacement, and φ sets the starting point.
Real-world uses
- Describing sound waves and musical notes mathematically.
- Modelling the position of a pendulum bob over time.
- A mass on a spring moves in a sine-shaped pattern in time, which is the basis for analysing many vibrations.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What is φ?
The phase constant, which sets where the motion starts in its cycle.
Can I use sine instead of cosine?
Yes, the choice only changes the phase constant.
What do the amplitude and phase constant mean?
The amplitude is the maximum displacement, and the phase constant sets where the motion starts in its cycle.
Related topics in Oscillations & SHM
Oscillatory motion · Period, frequency, amplitude · Simple harmonic motion · SHM velocity · SHM acceleration · Angular frequency