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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