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SHM displacement formula

The shm displacement formula as it is used in A Level Physics, taken from the A Level Physics formula sheet.

The formula

x=Acos⁡(ωt)x = A\cos(\omega t)

How to use it in the exam

  • Write the formula down before substituting — most mark schemes award a method mark for a correct, clearly quoted formula.
  • Check every quantity is in consistent units before you substitute, then substitute in one step so the working stays easy to follow.
  • Show the rearrangement rather than jumping to the answer, and give the final value to the accuracy the question asks for.

Related circular motion & shm formulas

Angular speed
ω=2πT=2πf\omega = \dfrac{2\pi}{T} = 2\pi f
Centripetal acceleration
a=v2r=ω2ra = \dfrac{v^2}{r} = \omega^2 r
Centripetal force
F=mv2r=mω2rF = \dfrac{mv^2}{r} = m\omega^2 r
SHM defining equation
a=−ω2xa = -\omega^2 x
Period of a mass–spring
T=2πmkT = 2\pi\sqrt{\dfrac{m}{k}}
Period of a pendulum
T=2πlgT = 2\pi\sqrt{\dfrac{l}{g}}

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