Question

Objects A and B are in harmonic motion modeled by

yA = 8 sin(2t − π/3) and yB = 8 sin(2t − π/4)

The phase difference between yA and yB is ....?

Answer 1

The phase difference between yA and yB is
`(-\pi )/(12)`

Explanation:

Given harmonic modeled as :

yA = 8 sin(2t -
`(\pi )/(3)`) And

yB = 8 sin(2t -
`(\pi )/(4)`)

The function as written as :

y = a sin(ωt - Ф) where Ф is phase difference

So , phase difference between yA and yB = ( Ф_1 - Ф_2 )

Or phase difference between yA and yB = ( -
`(\pi )/(3)` +
`(\pi )/(4)` )

Or, phase difference between yA and yB =
`((-4\pi +3\pi )/(12))`

I.e phase difference between yA and yB =
`(-\pi )/(12)`

Hence The phase difference between yA and yB is
`(-\pi )/(12)` Answer

Answer 2

-π/12

Explanation:

yA has a phase shift of -π/3; yB has a phase shift of -π/4. The difference between their phases is ...

-π/3 -(-π/4) = (-4/12 +3/12)π = -π/12

yA lags yB by π/12 radians.