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Lecture

# November 1.doc

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School
Department
Physics
Course
PHYS 101
Professor
Kenneth Ragan
Semester
Fall

Description
Phys 101 Alanna Houston November 1, 2007 - Pendulum is simple example of SHM: - - The period of a pendulum depends on: its length and g. o Displacement along arc: o Restoring force: o But for small angles: , therefore, o The period T will be: o The frequency would be: o The period DOES NOT depend on amplitude or mass o However, if the amplitude is very large, it would have a small effect because we just assumed that sine of theta was approximately theta - What would happened if you could dig a hole through the centre of the earth (ignore air resistance)? o It would get to the far side and drop back in o Has potential at beginning and not at the end therefore it is moving at the centre (KE). It will go until all potential energy is reclaimed. Therefore it would undergo simple harmonic motion through the centre of the earth. - Example: Bungee jumper, 65.0 kg. After jumping, he oscillates, hitting low point 8 times in 38.0 seconds. Finally comes to rest 25.0 m below bridge. What is k and unstretched length of the cord? o T = 38/8 o f = 1/T = 8/38 o f = 1/2pi(sqrt(k/m)) o k = (2pif)^2 * m o k = 114 N/m Phys 101 Alanna Houston o mg = kx o x = mg/k, x = (65*9.8)/114 = 5.6 m o 25 – 5.6 = length, length of cord = 19.4 m - Example: What length of pendulum is necessary for a swing every second; ie. T = 2.0s o 2.0 = 2pi(sqrt(L/g)) o L = (1/pi)^2 * g o 9.8/pi^2 = 0.993 m Resonance (forced vibrations): - SHM (springs and pendulums) have natural oscillation frequencies: - - If you nudge one of these systems, we will have SHM with a natural frequency f o - If we drive it by implying a periodic impulse or force at some arbitrary frequency f, it will not swing at f , out at f instead. - Amplitude however will depend on the difference between f and f o but will be largest when f = o. - This is called resonance and natural frequency is often called resonant frequency: - - Pros and cons: o Tacoma Narrows Bridge o Feedback in electrical circuits o Resonance in musical instruments - On a swing, you push them to increase amplitude* Summary of SHM relations: - SHM results in sinusoidal curves for displacement, velocity, acceleration: - In general, - For a spring: Phys 101 Alanna Houston - o no dependance on amplitude - For a pendulum at small amplitude: - o no dependance on amplitude or mass WAVES AND WAVE MOTION Transverse Waves: - The sources of waves are always a vibration or oscillation - If the source is vibrating with SHM, then the wave generated would have a sinusoidal shape in space and time - Wave propagates along the rope but the rope moves side to side - Medium does not move in the same way as the wave - Waves like this do NOT transport matter/mass but do transfer energy - - The wave velocity in a stretched string or cord depends on s
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