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

y1=a sin ωt and y2= b cos ωt =-b sin ωt+π2Since the frequencies for both SHMs are same, resultant motion will be SHM. NowAmplitude A=A12+A22+2A1A2 cos θ Here        A1=a,A2=b and ϕ=π2So           A=a2+b2 Aa2+b2