PHY221 Ch21: SHM

1. Main Points: • Spring force and simple harmonic motion in 1d• General solution a Cos wt+f• Plot x, v, a

2. Example• Vertical spring with mass and oscillation around equilibrium• Why are springs important: Systems close to equilibrium

PHY221 Ch21: SHM1.

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1.1 Spring force and simple harmonic motion in 1d

PHY221 Ch21: SHM1.

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1.1 Spring force and simple harmonic motion in 1d

PHY221 Ch21: SHM1.

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1.2 General solution a Cos wt+f

PHY221 Ch21: SHM1.

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1.3 Plot x, v, a

PHY221 Ch21: SHM2.

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2.1 Vertical spring with mass and oscillation around equilibrium

Now let’s look at a spring and mass m hanging from, say, the ceiling:

PHY221 Ch21: SHM2.

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2.2 Why are springs important (cont’d)

Comment on Taylor series expansion:

a. Preliminaries: quadratic approximation of a function U(x) around a value xe

PHY221 Ch21: SHM2.

Exam

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2.2 Why are springs important: Systems close to equilibrium

PHY221 Ch21: SHM2.

Exam

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2.1 Vertical spring with mass and oscillation around equilibrium