Question

When two displacements represented by y₁ = a sin ωt and y₂ = b cos ωt are superimposed, then the motion is

(a) Not a simple harmonic

(b) Simple harmonic with amplitude a/b

(c) Simple harmonic with amplitude \(\sqrt{(a^2 + b^2)}\)

(d) Simple harmonic with amplitude \((\frac{a + b}{2})\)

Answer 1

Given y₁ = a sin ωt

y₂ = b sin ωt

= b sin (ωt + \(\frac{\pi}{2}\))

The resultant displacement is given by

y = y₁ + y₂

_{\( = \sqrt{(a^2 + b^2)}sin(\omega t +\phi )\)}

Hence the motion of superimposed wave is simple

harmonic with amplitude \(\sqrt{(a^2 + b^2)}\)