When two displacement represented by y1

1. A

2. B

   Simple harmonic with amplitude ab

3. C

   Simple harmonic with amplitude a2+b2

4. D

   Simple harmonic with amplitude (a+b)2

The two displacement equations are y1 = a sin(ωt) and y2 = b cos(ωt) = b sin(ωt+π2)

yeq = y1+y2

      = a sin ωt + b cos ωt

       = a sin ωt + b sin (ωt+π2)

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

Now Aeq = a2+b2+2abcosπ2

⇒Aeq = a2+b2