Phase simply means an angular term which represents situation of a particle in SHM at a certain instant
Let one SHM is
x1=Asinωt and another SHM which is differ by first SHM of phase angle
ϕ then other SHM is,
x2=Asin(ωt+ϕ)
Clear that phase of oscillation is state of oscillation of particle performing SHM.
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