Answer :

We know here we are given equation of simple harmonic motion as


x = 3 sin (2πt + π/4)


Converting to Cosine


Using Cos(𝜽 + π/2) = Sin𝜽


We get


x = 3 cos (2πt + π/4 + π/2) = 3 Cos (2πt + 3π/4)


or we get


x = 3 Cos (2πt - π/4)


now comparing it with standard equation of S.H.M


x = A cos(ωt + ϕ)


where x is the position of particle in time t moving in S.H.M. with angular frequency ω and ϕ is the initial phase angle, A is the amplitude


clearly since here coefficient of cosine term is 3 so amplitude is 3 cm i.e radius of circle will be 3 cm


now initial position of particle or position at t = 0 sec will be


x = 3 sin (0 + π/4) = 3Sin(π/4)


i.e. (since )


i.e x component of displacement of particle is in positive x direction


the coefficient of t is angular velocity so here the angular velocity is


ω = 2π rad/s


we have to assume particle to be moving in anticlockwise direction


and initial phase angle is


ϕ = -π/4 = -450


i.e. line joining centre of circle to position of particle makes angle of 450 with x axis in clockwise sense


so the plot is as shown in figure



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