Lecture 3 - Osc. Motion (Ch 12.7-12.8)

# Lecture 3 - Osc. Motion (Ch 12.7-12.8) - Lecture 3:...

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Lecture 3: Harmonic Motion & Pendulums

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Energy and Springs Q: We know that in the absence of outside forces, the energy in the spring is conserved => E_total is constant. What is this constant? potential kinetic
Energy and Springs Q: We know that in the absence of outside forces, the energy in the spring is conserved => E_total is constant. What is this constant?

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Energy and Springs Space and velocity “solutions” for x(t) and v(t) for a mass on a spring.
Energy and Springs

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Using Energy Conservation w/ springs o Energy conservation can be very helpful for solving some problems If the problem doesn’t involve time directly o Strategy: Find the total energy E (it doesn’t change) Use a known kinetic energy (v) to solve for unknown potential energy (x), or Use a known potential energy (x) to solve for unknown kinetic energy (v) e.g. HW problem 8 this week [ch 12.P.015]
Energy Conservation is Your Friend o Energy conservation allowed us to solve the previous example because it didn’t ask about any specific time It asked: “what is the speed when the displacement is. ..” A similar type of problem could ask: “what is the displacement when the speed is . ..” o Learn to recognize problems that don’t involve time explicitly, and use energy conservation to solve them

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Simple Harmonic Motion Simple harmonic motion is described by cosine or sine function: A is the amplitude, φ is the “phase”. ω is the angular frequency Increase A Change φ Change ω
Example Simple Harmonic Motion A mass on a spring The frequency of oscillation is set by the spring constant (k) and mass of the block (m).

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2nd Example: Simple Pendulum As with the spring, the frequency of oscillation will depend only on properties of the system -- not on initial conditions.
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## This note was uploaded on 09/08/2008 for the course PHYS 3B taught by Professor Wu during the Spring '08 term at UC Irvine.

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Lecture 3 - Osc. Motion (Ch 12.7-12.8) - Lecture 3:...

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