Oscillations are one of the most prevalent phenomena in our universe. From a swinging tree branch, to molecular vibrations, even to the orbits of celestial bodies, repetitive events happen everywhere in nature. Simple harmonic oscillators (SHO) are specific type of oscillation where the motion can be described by sinusoidal functions and the time per revolution (period) is independent of the amplitude of the vibration.
Here is a quick introduction of Harmonic Motion
Big Ideas
Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure.
Bid Idea 2: Fields existing in space can be used to explain interactions.
Big Idea 3: The interactions of an object with other objects can be described by forces.
Big Idea 4: Interactions between systems can result in changes in those systems.
Big Idea 5: Changes that occur as a result of interactions are constrained by conservation laws.
Big Idea 6: Waves can transfer energy and momentum from one location to another without the permanent transfer of mass and serve as a mathematical model for the description of other phenomena.
Big Idea 7: The mathematics of probability can be used to describe the behavior of complex systems and to interpret the behavior of quantum mechanical systems.
Learning Objectives
BoxSand Learning Objectives
- Waves-Ocillations.SHO.LO.BS.1: Be able to identify the features of a system that oscillates - i.e. systems with a restoring force and a potential energy well
- Waves-Ocillations.SHO.LO.BS.2: Be able to identify if an oscillation will be Simple Harmonic - i.e. systems with a linear restoring force and a quadratic potential energy well
- Waves-Ocillations.SHO.LO.BS.3: Apply the sinusoidal equations of motion (position, velocity, acceleration) to SHO - i.e. fit them to the system using the initial conditions
- Waves-Ocillations.SHO.LO.BS.4: Understand the universal physical quantities of a SHO
- Waves-Ocillations.SHO.LO.BS.5: Understand the system specific (springs and pendulums) physical quantities
College Board Learning Objectives
- Waves-Ocillations.SHO.LO.CB.3.B.3.1: The student is able to predict which properties determine the motion of a simple harmonic oscillator and what the dependence of the motion is on those properties. [SP 6.4, 7.2]
- Waves-Ocillations.SHO.LO.CB.3.B.3.2: The student is able to design a plan and collect data in order to ascertain the characteristics of the motion of a system undergoing oscillatory motion caused by a restoring force. [SP 4.2]
- Waves-Ocillations.SHO.LO.CB.3.B.3.3: The student can analyze data to identify qualitative or quantitative relationships between given values and variables (i.e., force, displacement, acceleration, velocity, period of motion, frequency, spring constant, string length, mass) associated with objects in oscillatory motion to use that data to determine the value of an unknown. [SP 2.2, 5.1]
- Waves-Ocillations.SHO.LO.CB.3.B.3.4: The student is able to construct a qualitative and/or a quantitative explanation of oscillatory behavior given evidence of a restoring force. [SP 2.2, 6.2]
Enduring Understanding and Essential Knowledge
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Enduring Understanding |
Essential Knowledge |
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Waves-Ocillations.SHO.EU.CB.3.B: Classically, the acceleration of an object interacting with other objects can be predicted by using $\vec{a} = \frac{\sum \vec{F}}{m}$. |
Waves-Ocillations.SHO.EK.CB.3.B.3: Restoring forces can result in oscillatory motion. When a linear restoring force is exerted on an object displaced from an equilibrium position, the object will undergo a special type of motion called simple harmonic motion. Examples include gravitational force exerted by the Earth on a simple pendulum and mass-spring oscillator.
Relevant Equations: $T_{p}= 2 \pi \sqrt{\frac{m}{k}}$ |
Assumptions
Describe what the assumptions are and why they're important
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History
History
Physics Fun
Fun stuff
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