List of top Physics Questions on Simple Harmonic Motion and Uniform Circular Motion

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).
  1. x = –2 sin (3t + \(\frac{\pi}{3}\))
  2. x = cos (\(\frac{\pi}{6}\) – t)
  3. x = 3 sin (2πt + \(\frac{\pi}{4}\))
  4. x = 2 cos πt 

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

Figure 14.30 (a) shows a spring of force constant k clamped rigidly at one end and a mass attached to its free end. A force F applied at the free end stretches the spring. Figure 14.30 (b) shows the same spring with both ends free and attached to a mass m , then clamped rigidly at one end and a mass at either end. Each end of the spring in Fig. 14.30(b) is stretched by the same force F.

maximum extension of the spring in the two cases

What is the maximum extension of the spring in the two cases? 

If the mass in Fig. (a) and the two masses in Fig. (b) are released, what is the period of oscillation in each case?