Consider the system shown at the right with a spring attached to a support. It may not be surprising that it is a wiggle of this general sort, but why is it a specific mathematically perfect shape? Every time the spring is compressed or stretched relative to its relaxed position, there is an increase in the elastic potential energy. H decides to use a little physics for better living.

The Physical Pendulum The period of a physical pendulum depends upon its moment of inertia about its pivot point and the distance from its center of mass. Centripetal acceleration is of constant magnitude and directed at all times towards the center of the circle.

## Simple Harmonic Motion: A Special Periodic Motion

For illustration, let us consider a uniform rigid rod, pivoted from a frame as shown see. A rigid rod with uniform mass distribution hangs from a pivot point. The shadow undergoes simple harmonic motion. Learning Objectives Relate the restoring force and the displacement during the simple harmonic motion. This blending of the concepts would lead us to conclude that the kinetic energy of the mass on the spring increases as it approaches the equilibrium position; and it decreases as it moves away from the equilibrium position.

Learning Objectives Identify parameters that affect the period of a physical pendulum. If the length of a pendulum is precisely known, it can actually be used to measure the acceleration due to gravity. Some people modify cars to be much closer to the ground than when manufactured.

For small amplitudes, the period of such a pendulum can be approximated by:. The word period refers to the time for some event whether repetitive or not; but we shall be primarily interested in periodic motion, which is by definition repetitive. The maximum velocity depends on three factors: Learning Objectives Describe relationship between the simple harmonic motion and uniform circular motion.

A hypothetical pendulum consisting of a weight suspended by a weightless string. A variable force that gives rise to an equilibrium in a physical system. As you might guess, the greater the maximum displacement, the greater the maximum velocity.

## Simple Harmonic Motion (SHM)

Force and stretch are proportional to one another such that if you double the force, the amount of stretch will double. The period is completely independent of other factors, such as mass. The glider will be pulled to the right of its equilibrium position and be released from rest position A.