Oscillatory motion is a repetitive motion back and forth around an equilibrium position. We’ll describe oscillations in terms of their amplitude, period, and frequency. The most important oscillation is simple harmonic motion (SHM), where the position and velocity graphs are sinusoidal.

The prototype of SHM is a mass oscillating on a spring. Lessons learned from this system apply to all SHM.

• A pendulum is a classic example of SHM.

• Any system with a linear restoring force undergoes SHM.

《 LOOKING BACK Section 9.4 Restoring forces

The projection of uniform circular motion onto a line oscillates back and forth in SHM.

• This link to circular motion will help us develop the mathematics of SHM.

• A phase constant, based on the angle on a circle, will describe the initial conditions.

《 LOOKING BACK Section 4.4 Circular motion

If there is no friction or other dissipative force, the mechanical energy of an oscillating system is conserved. Energy is transformed back and forth between kinetic and potential energy. Energy conservation is an important problem-solving strategy.

《 LOOKING BACK Sections 10.3, 10.4, and 10.5 Elastic potential energy and energy diagrams

If there’s dissipation, the system “runs down.” This is called a damped oscillation. The oscillation amplitude undergoes exponential decay. But the amplitude can grow very large when an oscillatory system is driven at its natural frequency. This is called resonance.

Simple harmonic motion is one of the most common and important motions in science and engineering.

• Oscillations and vibrations occur in mechanical, electrical, chemical, and atomic systems. Understanding how a system might oscillate is an important part of engineering design.

• More complex oscillations can be understood in terms of SHM.

• Oscillations are the sources of waves, which we’ll study in the next two chapters.