A particle executing SHM of amplitude 'a' has a displacement a/2 at t = T/4 and a negative velocity. The epoch of the particle is

Equation of SHM =ysin⁡(ωt+ϕ) When y=a2,t=T4=2π4ω=π2ωv=aωcos⁡(ωt+ϕ) velocity is negativeπ2<(ωt+ϕ)<3π2a2=asin⁡(ωt+ϕ) ⇒sin⁡(ωt+ϕ)=12π2+ϕ=5π6 Substituting in the above equation, we get ϕ=π/3