A particle is performing a linear simple harmonic motion. If the acceleration and the corresponding velocity of the particle are a and v respectively, which of the following graphs is correct?

detailed solution

Correct option is C

If a particle performs SHM with angular frequency 'ω' and amplitude 'A' then its displacement from mean position will be equal to x = a sin ωt. If its initial phase is equal to zero, velocity will bev = dxdt=Aω cosωt------(i)and acceleration will bea= dvdt = -Aω2sin(ωt)------(ii)From these equations,cos ωt = vAω, sin ωt = a-Aω2Squaring and adding,v2A2ω2+a2A2ω4 = 1If ‘v’ taken on y-axis and a on x-axis, then it will be an ellipse.