Simple Harmonic Motion (SHM)

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# Simple Harmonic Motion (SHM) - PowerPoint PPT Presentation

Simple Harmonic Motion (SHM). (and waves). What do you think Simple Harmonic Motion (SHM) is???. Defining SHM. Equilibrium position Restoring force Proportional to displacement Period of Motion Motion is back & forth over same path. Θ. F g. Describing SHM. Amplitude. Θ. F g.

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## PowerPoint Slideshow about 'Simple Harmonic Motion (SHM)' - freira

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Presentation Transcript

### Simple Harmonic Motion (SHM)

(and waves)

Defining SHM
• Equilibrium position
• Restoring force
• Proportional to displacement
• Period of Motion
• Motion is back & forth over same path

Θ

Fg

Describing SHM
• Amplitude

Θ

Fg

Describing SHM
• Period (T)
• Full swing
Frequency
• Frequency- Number of times a SHM cycles in one second (Hertz = cycles/sec)
• f = 1/T
SHM Descriptors
• Amplitude (A)
• Distance from start (0)
• Period (T)
• Time for complete swing or oscillation
• Frequency (f)
• # of oscillations per second
Oscillations
• SHM is exhibited by simple harmonic oscillators (SHO)
• Examples?
Examples of SHOs
• Mass hanging from spring, mass driven by spring, pendulum
SHM for a Pendulum
• T = period of motion (seconds)
• L = length of pendulum
• g = 9.8 m/s2
EPE = ½ k x2
• KE = ½ m v2
• E = ½ m v2 + ½ k x2
• E = ½ m (0)2 + ½ k A2E = ½ k A2
• E = ½ m vo2 + ½ k (0)2E = ½ m vo2

Velocity
• E = ½ m v2 + ½ k x2
• ½ m v2 + ½ k x2 = ½ k A2
• v2 = (k / m)(A2 - x2) = (k / m) A2 (1 - x2 / A2)
• ½ m vo2 = ½ k A2
• vo2 = (k / m) A2
• v2 = vo2 (1 - x2 / A2)
• v = vo 1 - x2 / A2
Damped Harmonic Motion
• due to air resistance and internal friction
• energy is not lost but converted into thermal energy
Damping
• A: overdamped
• B: critically damped
• C: underdamped
Resonance
• occurs when the frequency of an applied force approaches the natural frequency of an object and the damping is small (A)
• results in a dramatic increase in amplitude