1.1: Periodic Motion and Simple Harmonic Oscillators
Simple harmonic motion refers to a repetitive movement back and forth through an equilibrium, or central position, so the maximum displacement on one side of this position equals the maximum displacement on the other side. Therefore, the time interval of each complete vibration is the same.
Simple harmonic motion arises when a restoring force appears in a system, when that system is disturbed from equilibrium, and when the force is proportional to and has the opposite direction of the displacement.
This proportionality is called Hooke's Law. A typical example of a system obeying Hooke's Law is a point mass attached to the end of a massless spring. The spring exerts a restoring force on the mass that tries to return the spring to its natural, unstrained length. The length by which the spring is stretched or compressed is the displacement that Hooke's Law refers to. We also call this the deformation, or elongation. The strength of the restoring force for a given displacement is characterized by a spring constant, which is determined by the material of the spring and how tightly it is wound.
Before we begin, watch this video that explains why it is important to study electromagnetism. There are two types of charges, and like charges repel, while unlike charges attract. When equal amounts of both charge types are combined in an object, it becomes electrically neutral. The forces from balanced charges of opposite types inside a neutral object cancel out when viewed from the outside. This explains why we do not often notice the effects of electromagnetism directly, which creates the impression that it must be a weak kind of force. In reality, electric forces are much stronger than gravity! We will come back to this in later lectures.
Read this introduction to Hooke's Law that covers the concept of energy. Using the language of energy, deformed springs store potential energy, which can be converted into kinetic energy when the spring is released. In this process, the spring force causes acceleration by doing mechanical work.
When a spring causes acceleration, the motion often overshoots the equilibrium that it wants to return to because the oscillating mass has inertia. After it overshoots, the restoring force reverses direction and causes an opposite acceleration. This is how oscillations are created: the motion keeps reversing and overshoots its equilibrium every time.
Read this text to learn how we characterize oscillations quantitatively. The standard unit of frequency is called hertz (abbreviated Hz). It is no coincidence that you find the same unit labeling your radio dial: later, we will see that radio stations transmit electromagnetic waves of specific frequencies.