Physics

Problem

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

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, by considering the argument of the sine function, that the quantity

\sin(\omega t + \phi)

is dimensionless. (iii) Verify that the given equation is dimensionally consistent in each term. b. (ii) Show that

\sin(\omega t + \phi)

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