Velocity and Acceleration in Simple Harmonic Motion

Plot the corresponding reference circle for 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 + π/3)

The average acceleration in one time period in a simple harmonic motion is

Show that for a particle executing S.H.M, velocity and displacement have a phase difference of π/2.

Plot the corresponding reference circle for 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 π t

A thin circular ring of mass M and radius R is rotating with a constant angular velocity of 2 rads^-1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity (in rads^-1).

Two massless springs with spring constants 2k and 9k carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be ______.

The free end of a simple pendulum is attached to the ceiling of a box. The box is taken to a height and the pendulum is oscillated. When the bob is at its lowest point, the box is released to fall freely. As seen from the box during this period, the bob will

Plot the corresponding reference circle for 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 `(2πt + π/4)`