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))`

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 =-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 =3 sin (2pit+(pi//4))

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.

Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (co is any positive constant):exp (-omega^2t^2)

The motion of a particle of mass m is given by x = 0 for t 0), and x = 0 for t > (1/4) s. which of the following statements is true?/

Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (co is any positive constant): 1 +omegat +omega^2t^2

Force on a charge in electric and magnetic fields A charge particle follows a parabolic path in a uniform electric field and a charged particel moving in a uniform magnetic field has two kinds of motions lnear motion in the direction of magnetic field and circular motion in a plane perpendicular to the magnetic field. when charge q is moving perpendicular to the magnetic field B, the radius of the circular path is r=(mv)/(Bq) . If v and B makes an angle theta , then r=(mvsintheta)/(Bq) , and the time period T=(2pim)/(Bq) . Under the influenece of a uniform magnetic field, a charged particles is moving in a circle of radius r with speed v. The time period of motion.

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.