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). x =-2 sin `(3t+(pi//3))`

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). x=2 cos pi t

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). x =3 sin (2pit+(pi//4))

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). x= cos (pi//(6-t))

The motion of a particle executing simple harmonic motion is described by the displacement function, x(t) = A cos (omegat + phi) . If the initial (t = 0) position of the particle is 1 cm and its initial velocity is omega cm//s , what are its amplitude and initial phase angle ? The angular frequency of the particle is pi s^-1 s If instead of the cosine function, we choose the sine function to describe the SHM : x= B sin (omegat+alpha) , what are the amplitude and initial phase of the particle with the above initial conditions.

In the figure gives the (x-t) plot of a particle executign one-dimensional simple harmonic motion. Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, - 1.2 s.

The equation of a simple harmonic wave is given by y=3 sin pi/2 (50 t-x) where x and y are in mtres and t is in seconds.The ratio of maximum particle velocity to the wave velocity is :

If the pair of lines sqrt(3)x^(2)-4xy+sqrt(3)y^(2)=0 is rotated about the origin by pi//6 in the anticlockwise sense , then find the equation of the pair of lines in the new position.

Figure 3.23 gives the x-t plot of a particle executing one-dimensional simple harmonic motion. (You will learn about this motion in more detail in Cliapterl4). Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, - 1.2 s.

Figure 3.21 shows the x-t plot of one-dimensional 4 motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for t 0 ? If not, suggest a suitable physical context for this graph.

The velocity-time graph of a particle in one-dimensional motion is shown in Fig. 3.29 :- Which of the following formulae are correct for describing the motion of the particle over the time-interval:- x(t_2)-x(t_1) area under the v-t curve bounded by the t-axis and the dotted line shown.