When two displacements represented by ${\mathrm{y}}_1=\mathrm{asin}\left(\mathrm{\omega t}\right)$ and ${\mathrm{y}}_2=\mathrm{b} \cos \left(\mathrm{\omega t}\right)$ are superimposed the motion is

• A

  $\text{ simple harmonic with amplitude }\sqrt{{\mathrm{a}}^2+{\mathrm{b}}^2}$

• B

  $\text{ simple harmonic with amplitude }\frac{(\mathrm{a}+\mathrm{b})}{2}$

• C

  not a simple harmonic

• D

  $\text{ simple harmonic with amplitude }\frac{\mathrm{a}}{\mathrm{b}}$