Show that the motion of a particle represented by y= sin ωt- cos ωt is simple harmonic with a period of 2π/ω.

Hint: It should be a periodic function comparable to the standard equation of motion.
Step 1: Find the equation of a single SHM.
We have to convert the given combination of two harmonic functions to a single harmonic (sine or cosine) function.
Given, displacement function,            y= sinωt - cosωt
                                                      =212·sinωt-12·cosωt
=2cosπ4·sinωt-sinπ4·cosωt
=2sinωt-π4
Step 2: Find the time period of the oscillation.
Comparing it with the standard equation, y=asin(ωt+ϕ),
we get, ω=2πTT=2πω
Clearly, the function represents SHM with a period T=2πω.