Periodic and Oscillatory Motion

A person normally weighing 50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 2.0 s^–1 and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time.

1. Will there be any change in weight of the body, during the oscillation?
2. If answer to part (a) is yes, what will be the maximum and minimum reading in the machine and at which position?

A copper metal cube has each side of length 1 m. The bottom edge of the cube is fixed and tangential force 4.2x10⁸ N is applied to a top surface. Calculate the lateral displacement of the top surface if modulus of rigidity of copper is 14x10¹⁰ N/m².

Which of the following example represent periodic motion?

A hydrogen molecule rotating about its center of mass.

A small block of mass m is kept on a bigger block of mass M which is attached to a vertical spring of spring constant k as shown in the figure. The system oscillates vertically. (a) Find the resultant force on the smaller block when it is displaced through a distance x above its equilibrium position. (b) Find the normal force on the smaller block at this position. When is this force smallest in magnitude? (c) What can be the maximum amplitude with which the two blocks may oscillate together?

When a particle executes Simple Harmonic Motion, the nature of the graph of velocity as a function of displacement will be ______.

Show that the motion of a particle represented by y = sin ωt – cos ωt is simple harmonic with a period of 2π/ω.

A simple pendulum of frequency n falls freely under gravity from a certain height from the ground level. Its frequency of oscillation.

Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?

General vibrations of a polyatomic molecule about its equilibrium position.