The displacement of a particle varies with time according to the relation y = a sin ωt + b cos ωt a) the motion is oscillatory but not SHM b) the motion is SHM with amplitude a + b c) the motion is SHM with amplitude a2 + b2 d) the motion is SHM with amplitude √a2 + b2
Correct option is D) Given x=asinωt+bcosωt .......(i) Let a=Acosϕ ........(ii) and bAsinϕ ..........(iii) Squaring adding (ii) and (iii), we get a2+b2=A2cos2ϕ+A2sin2ϕ=A2 Eq.(i) can be written as x=Acosϕsinωt+Asinϕcosωt=Asin(ωt+ϕ) It is equation of SHM with amplitude A=√a2+b2
