Q. 12 A4.1( 7 Votes )

Plot the correspo

Answer :

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


x = –2 sin (3t + π/3)


Converting to Cosine


Using Cos(π/2+𝜽) = -Sin𝜽


We get


x = –2 sin (3t + π/3) = 2 Cos (3t + π/3 + π/2)


or we get


x = 2 cos (3t + 5π/6)


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 2 so amplitude is 2 cm i.e radius of circle will be 2 cm


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


x = -2 sin (0 + π/3) = -2Sin(π/3)


i.e. (since )


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


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


ω = 3 rad/s


we have to assume particle to be moving in anticlockwise direction


and initial phase angle is


ϕ = 5π/6 = 1500


i.e. line joining centre of circle to position of particle makes angle of 1500 with x axis in anticlockwise sense


so the plot is as shown in figure



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