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 = -45^{0}

i.e. line joining centre of circle to position of particle makes angle of 45^{0} with x axis in clockwise sense

**so the plot is as shown in figure**

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