Two particles oscillate in simple harmonic motion along a common straight-line segment of length

a. each particle has a period of 1.5 s, but they differ in phase by pi/6 rad. (a) how far apart are they (in terms of

a. 0.50 s after the lagging particle leaves one end of the path

Assuming the two functions are sine functions.

From the problem:

T = 1.5

So

b = 2π/T

b = 2π/1.5

b = 4π/3

The first sine function has an equation

y1 = sin 4π/3x

and since they have a difference in phase of π/6, the other sine function has an equation

y2 = sin 4π/3x + π/6

Their difference is simply π/6.

If we substitute 0.5 s to each equation,

y1 = 2π/3

y2 = 5π/6