Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial (t =0) position of the particle, the radius of the circle, OSCILLATIONS 365 and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: (x is in cm and t is in s). (a) x = –2 sin (3t + π /3) (b) x = cos (π /6 – t) (c) x = 3 sin (2π t + π /4) (d) x = 2 cos π t

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Solution

a)

The equation of motion of simple harmonic motion is,

Rearrange the terms of equation.

(1)

The general equation of SHM is given by,

(2)

After comparing the equation (1) and equation (2), we get

The motion of the particle is plotted as,

b)

The equation of motion of simple harmonic motion is,

x=cos( π 6 −t )

Rearrange the terms of equation.

(3)

After comparing the equation (3) and equation (2), we get

The motion of the particle is plotted as,

c)

The equation of motion of simple harmonic motion is,

Rearrange the terms of equation.

(4)

After comparing the equation (4) and equation (2), we get

The motion of the particle is plotted as,

d)

The equation of motion of simple harmonic motion is,

After comparing the given equation with equation (2), we get

The motion of the particle is plotted as,

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Similar questions

Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial (t = 0) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: (x is in cm and t is in s).

(a) x = –2 sin (3t + π/3)

(b) x = cos (π/6 – t)

(d) x = 2 cos πt

Q. Figure shows the circular motion of a particle. The radius of the circle, the time period

T

, sense of revolution and the initial position are indicated in the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle

P

Q. Figure shows the circular motion of a particle. The radius of the circle, the time period

T

, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle

P

Q. Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated in the figure. The simple harmonic motion of the

x

- projection of the radius vector of the rotating particle P is

Figures 14.29 correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure.

Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each case.

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