DO NOW QUESTION Which of these is harmonic motion – a child swinging on a swing or a wagon rolling down a hill?

Systems and equilibrium Systems that have harmonic motion always move back and forth around a central, or equilibrium position.

SWBAT explain how harmonic motion is maintained. Objective 3/12/14 SWBAT explain how harmonic motion is maintained.

Unit 7: Vibrations, Waves & Sound Chapter 18: Harmonic Motion 18.2 Graphs of Harmonic Motion 18.3 Properties of Oscillators

Systems and equilibrium Systems that have harmonic motion always move back and forth around a central, or equilibrium position. In equilibrium, there is a net force of 0N.

Restoring force A restoring force is any force that always acts to pull a system back toward equilibrium.

Restoring force and inertia The restoring force is related to the weight of the mass (or gravity) and the lift force (or tension) of the string supporting the mass.

Inertia & Mass Systems oscillate naturally without external energy due to equilibrium, which follows Newton’s First Law – the Law of Inertia

Natural frequency and resonance The natural frequency is the frequency (or period) at which a system naturally oscillates. Every system that oscillates has a natural frequency.

Natural frequency Every oscillating system has a natural frequency. Microwave ovens, musical instruments, and cell phones are common devices that use the natural frequency of an oscillator. The strings of a guitar are tuned by adjusting the natural frequency of vibrating strings to match musical notes.

Natural frequency and resonance You can get a swing moving by pushing it at the right time every cycle. A force that is repeated over and over is called a periodic force.

Natural frequency and resonance Resonance happens when a periodic force has the same frequency as the natural frequency. When each push adds to the next one, the amplitude of the motion grows.

Jump rope A jump rope depends on resonance. Even if the force is strong, you must shake it at the right frequency to make a wave. If the frequency is too fast or too slow, the rope will not make the wave pattern at all.

Simple oscillators Shock Absorbers are springs in cars that are able to damper to slow down with bumps.

Simple oscillators A vibrating string oscillator is a rubber band stretched between two rods. If the middle of the rubber band is pulled to the side, it will move back toward equilibrium when it is released. Stretching the rubber band to the side creates a restoring force. When the rubber band is released, inertia carries it past equilibrium and it vibrates.

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Skyscrapers and Harmonic Motion The John Hancock Tower is one of the tallest skyscrapers in New England. While this skyscraper was being built in 1972 and 1973, a disaster struck— windowpanes started falling out all over the building and crashing to the ground.