Displacement x = $A\cos$($\omega$t)
Oscillations - OCR A-Level Physics
- DisplacementThe distance moved in a particular direction from a starting point. A vector quantityA quantity that has both magnitude and direction.. Measured in metres (m). x = $A\cos$($\omega$t): starts at maximum, passes through zero at T/4.
- VelocityThe rate of change of displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m).. A vector quantityA quantity that has both magnitude and direction.. Measured in m s⁻¹. v = -$A\omega\sin$($\omega$t): leads displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). $by \pi/2$ (quarter cycle). Maximum when x = 0.
- AccelerationThe rate of change of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantityA quantity that has both magnitude and direction.. Measured in m s⁻². a = -$A\omega$^$2\cos$($\omega$t): leads displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). $by \pi$(half cycle). In antiphase with displacement.
- AccelerationThe rate of change of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantity. Measured in m s⁻². and displacement are always in antiphaseTwo oscillations that are exactly half a cycle (π radians or 180°) out of phase.: when x is max positive, a is max negative.
- VelocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. and accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻². $are \pi/2$ out of phase: when v is max, a = 0 and vice versa.
- On a displacement-time graph: the gradient gives velocity, the gradient of the velocity-time graph gives accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻²..
Examiner Tips and Tricks
- When sketching graphs: displacement is cosine, velocity is negative sine, acceleration is negative cosine.
- Acceleration is an upside-down version of displacement.