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Simple Harmonic Motion
Simple Harmonic Motion
Simple Harmonic Motion is a simple type of oscillatory motion.
Simple Harmonic Motion is a simple type of oscillatory motion.
"Simple" represents the linear restoring force (e.g. spring).
"Harmonic" represents the motion that can be described as sine and cosine functions.
The Key requirement for an object to be experiencing SHM
The Key requirement for an object to be experiencing SHM
Restoring force always acts toward the equilibrium position and is directly proportional to the displacement from the equilibrium position (F∝-y )
Acceleration always acts toward the equilibrium position and is directly proportional to the displacement from the equilibrium position (𝑎=−𝜔^2 𝑦, or 𝑎∝−𝑦).
When an object is moving in simple harmonic motion (SHM)
When an object is moving in simple harmonic motion (SHM)
its speed is zero at the end points and maximum at the equilibrium position.
its acceleration is maximum at its end points and zeroes at the equilibrium position .
the force on it is always in the opposite direction to the displacement (and always towards the equilibrium position).
Properties of simple harmonic motion
Properties of simple harmonic motion
The amplitude of SHM is the maximum displacement from the equilibrium position.
Since the equilibrium position is halfway between end points, the amplitude is also half the distance between the end points.
The frequency of SHM is the number of complete oscillations per second.
The period of SHM is the time it takes for one complete oscillation.
SHM: Spring-Mass Oscillator
SHM: Spring-Mass Oscillator
Professor Dave Explains (4 min)
Simple Harmonic Motion
Simple Harmonic Motion
Bozeman Science (8 min)
Reference Circle and Sinusoidal Formulae
Reference Circle and Sinusoidal Formulae
Considering the relationship between SHM and circular motion: the movement of the shadow is simple harmonic motion; the position of the shadow can be calculated.
Comparing SHM to Circular Motion
Comparing SHM to Circular Motion
Flipping Physics (2 min)
SHM and Sinusoidal Function
SHM and Sinusoidal Function
Flipping Physics (3 min)
SHM and Sinusoidal Formulae
SHM and Sinusoidal Formulae
Flipping Physics (9 min)
Demo: SHM and Circular Motion
Demo: SHM and Circular Motion
Harvard Natural Sciences Lecture Demo (1 min)
Simulations and Animations - SHM
Simulations and Animations - SHM
SHM animation
SHM animation
Ya physics animations (1 min)
SHM: Pendulum animation
SHM: Pendulum animation
Ya physics animations (1 min)
SHM: Damped Pendulum animation
SHM: Damped Pendulum animation
Ya physics animations (1 min)
SHM Energy Simulator
SHM Energy Simulator
Damping SHM Simulator
Damping SHM Simulator
Forces Oscillation and Resonance
Forces Oscillation and Resonance
Resonance
Resonance
If the driving force has the same frequency as the nature frequency of the simple harmonic motion, the amplitude of the motion increases, often dramatically. When this happens, it is called resonance.
Examples:
Tacoma Narrows Bridge Collapse
Whine Noise from a car: Resonance effects can be a nuisance or cause damage (e.g. some cars develop a whine at a certain speed). The whine from a car is because the nature frequency of vibration of one of the car's panels just happens to be the same as the frequency of vibration of the engine. The resulting high-amplitude vibration of the panel creates a sound wave.
Tacoma Bridge Collapse
Tacoma Bridge Collapse
British Pathé (1 min)
Breaking Glass with Sound
Breaking Glass with Sound
MIT - Massachusetts Institute of Technology (1 min)
Why do buildings fall in earthquakes?
Why do buildings fall in earthquakes?
TED-Ed (5 min)
Graphing circular motion displacement (animated gif)
Displacement Phasor, wave and motion of mass or pendulum (Geogebra) GOOD!!!
reference circle concept vert and hoirz (Surendranath: use dropdown menu: oscillations: SHM)
Interactive reference circles (with sine vs cosine wave)
mass on spring (HKNG) with ref-circle & y, v, a vs t graphs
Ref-circle with mass on spring AND graph of y vs t (Surendranath: use dropdown menu: oscillations: phase-graph)
How kinetic and potential energy change with location or time (Surendranath: use dropdown menu: oscillations: mass-spring oscillations: then either K,U vs x or K,U vs t)
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