13.1 Harmonic Motion 1

Chapter 13 Objectives Identify characteristics of harmonic motion, such as cycles, frequency, and amplitude. Determine period, frequency, and amplitude from a graph of harmonic motion. Use the concept of phase to compare the motion of two oscillators. Describe the characteristics of a system that lead to harmonic motion. Describe the meaning of natural frequency. Identify ways to change the natural frequency of a system. Explain harmonic motion in terms of potential and kinetic energy. Describe the meaning of periodic force. Explain the concept of resonance and give examples of resonance. 2

Chapter 13 Vocabulary Terms amplitude damping frequency harmonic motion hertz (Hz) natural frequency oscillator period periodic force periodic motion phase phase difference piezoelectric effect resonance stable equilibrium unstable equilibrium

Inv 13.1 Harmonic motion Investigation Key Question: How do we describe the back and forth motion of a pendulum? 4

13.1 Cycles, systems, and oscillators A cycle is a unit of motion that repeats.

13.1 Harmonic motion is common sound communications clocks nature

13.1 Describing harmonic motion The period of an oscillator is the time to complete one cycle.

13.1 Describing harmonic motion Frequency is closely related to period. The frequency of an oscillator is the number of cycles it makes per second. At a frequency of 100 Hz, an oscillating rubber band completes 100 cycles per sec.

13.1 Describing harmonic motion The unit of one cycle per second is called a hertz (Hz). When you tune into a station at 100.6 on the FM dial, you are setting the oscillator in your radio to a frequency of 100.6 megahertz (MHz).

13.1 Amplitude Amplitude describes the size of a cycle. The value of the amplitude is the maximum amount the system moves away from equilibrium.

13.1 Amplitude The energy of an oscillator is proportional to the amplitude of the motion. Friction drains energy away from motion and slows the pendulum down. Damping is the term used to describe this loss.

13.1 Harmonic Motion Graphs Graphs of linear motion do not show cycles.

13.1 Harmonic motion graphs Graphs of harmonic motion repeat every period, just as the motion repeats every cycle. Harmonic motion is sometimes called periodic motion.

13.1 Circles and the phase of harmonic motion Circular motion is very similar to harmonic motion. Rotation is a cycle, just like harmonic motion. One key difference is that cycles of circular motion always have a length of 360 degrees.

13.1 Circles and the phase of harmonic motion The word “phase” means where the oscillator is in the cycle. The concept of phase is important when comparing one oscillator with another.