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

not a simple harmonic

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

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

simple harmonic with amplitude $\left(\frac{a+b}{2}\right)$