lecture16-damped oscillator

lecture16-damped oscillator - 100 200 300 400 500-10-5 5 10...

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What you can do so far … describe simple harmonic mo6on with graphs equa6ons for a perfect mass-spring AND pendulum What you will be able to do a>er today … the basic types of damped harmonic mo6on the phenomenon of resonance transversal vs. longitudinal waves Explain … the amplitude and/or energy of a damped oscillator the wave speed Calculate … determine the damping constant from a x(t) graph Apply …
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Damped Harmonic Motion Relate to graph: What ` s the blue curve? What ` s the dotted (exponential) line? x max ( t ) = Ae ! bt 2 m x ( t ) = Ae ! bt 2 m cos( ! ' t + " )
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Damped Harmonic Motion: Energy Real pendulum: Energy is not conserved, the energy as a function of time is given by Potential Energy: U = 1 2 kx max 2 ; x max ( t ) = Ae ! t 2 ! combine: E ( t ) = 1 2 k Ae ! t 2 ( ) 2 = 1 2 kA 2 " # $ % ' e ! t = E 0 e ! t
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The graph below shows simple harmonic motion with damping. The initial amplitude at t = 0 is 10 cm.
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Unformatted text preview: 100 200 300 400 500-10-5 5 10 Displacement (cm) Time (s) a)What is the frequency f of the oscillation? (a)0.5 Hz, (b) 0.6Hz, (c)0.05Hz, (d) 0.06Hz 100 200 300 400 500-10-5 5 10 Displacement (cm) b) What is the time constant τ ? Worksheet BONUS A 350 g block hangs from a spring with constant k = 23 N/m. The block is pulled down 5.5 cm from equilibrium, then released. a) Where is the block 1.5 s later (neglect damping)? b) What is its speed at t = 1.5 s (neglect damping)? c) BONUS: If the block loses half of its initial energy in 3.5 minutes, what is the damping constant of the system? d) How does the oscillation period compare for the undamped (T0) and the damped system (T)? (a) T< T0 (b) T>T0 (c) T=T0 (d) Not enough information....
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This note was uploaded on 01/15/2012 for the course PHYS 101 taught by Professor Bates during the Winter '08 term at UBC.

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lecture16-damped oscillator - 100 200 300 400 500-10-5 5 10...

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