Question:
Show that the motion of a particle represented by y = sin ωt – cos ωt is simple harmonic with a period of 2π/ω.
Solution:
A function will represent SHM and is written as sin (2π/T t + ϕ)
y = sin ωt – cos ωt
y = √2 sin (ωt – π/4)
The standard SHM has y = a s sin (2π/T t + ϕ)
T = 2π/ω