A mass–spring system executing simple harmonic motion is described by

PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

x = A \sin(\omega t + \phi)

, where

x

is the instantaneous displacement from equilibrium,

A

is the amplitude,

\omega

is the angular frequency and

\phi

is the initial phase. (i) State the dimensions of

A

and

x

. (ii) Show that

\sin(\omega t + \phi)

is dimensionless. (iii) Verify dimensional consistency of the equation.