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

Answer:

A function that represents SHM is written as

sin (2π/T t + ϕ)

We have, y = sin ωt – cos ωt

y = √2 sin (ωt – π/4)

The standard equation of SHM has:

y = a sin (2π/T t + ϕ)

Therefore, T = 2π/ω