When two displacements represented by y1 = a sin(ωt) and

When two displacements represented by y₁ = a sin(ωt) and y₂ = b cos(ωt) are super-imposed the motion is :

The two displacements equations are y₁ = a sin(ωt)

and y₂ = b cos(ωt) = b sin		ωt +	π
			2

y_eq = y₁ + y₂

= a sinωt + b cosωt = a sinωt + b sin		ωt +	π
			2

Since the frequencies for both SHMs are same, resultant motion will be SHM.

Now A_eq = √a² + b² + 2ab cos	π
	2

⇒ A_eq = √a² + b²

simple harmonic with amplitude	a
	b

simple harmonic with amplitude	(a + b)
	2