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Questions  

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

a
Not a simple harmonic
b
Simple harmonic with amplitude ab
c
Simple harmonic with amplitude a2+b2
d
Simple harmonic with amplitude (a+b)2

detailed solution

Correct option is C

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

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