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(26) Simple Harmonic Motion

# (26) Simple Harmonic Motion - Lecture 26 Simple Harmonic...

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Lecture 26 Simple Harmonic Motion

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Periodic motion Periodic motion A motion is called periodic when the system comes back to the same situation every time interval T. Same position Same ve locity Period Examples: Uniform circular motion Earth around the Sun Toy train in a circuit } π ϖ = = = 1 Fr equency 2 Angular 2 f requency f T f T
Oscillations about an equilibrium position Oscillations about an equilibrium position U x When a 1D system is re leased near a stable equilibrium point, the motion is periodic: oscillations between two turn-around points x 1 and x 2 . E x 1 x 2 Forbidden region Forbidden region Oscillations SE

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Simple Harmonic Motion (SHM) Simple Harmonic Motion (SHM) SHM is the oscillatory motion that happens when the restoring force is proportional to the displacement from the equilibrium position: F –x …or when the potential energy is a quadratic function of the displacement from the equilibrium position: U x 2 (a parabola) equivalent to
Example of SHM: Spring that obeys Hooke’s law = - F kx = 2 1 2 U kx Oscillations about x = 0 U x E –x 0 x 0

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(26) Simple Harmonic Motion - Lecture 26 Simple Harmonic...

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