Chapters 11 & 12

Chapters 11 & 12 - Periodic Motion Chapters 11 & 12...

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1 Chapters 11 & 12 Periodic Motion ± e.g. a pendulum - keeps swinging from side to side with a fixed period - hence we can use it to keep time (pendulum clock) ± it has an equilibrium position, but if we give it an initial push away from there, conservation of energy prevents it from coming to rest even though there is a force pulling it back ± simplest example of periodic motion is called simple harmonic motion – this turns out to be one of the most important idealizations in physics, it just keeps coming up • e.g. quantum field theories that describe the smallest known particles in the universe are really just fancy coupled harmonic oscillators Simple Harmonic Motion ± a physical system that is described well by simple harmonic motion is a glider on an air-track tethered by a spring ± free-body diagram of block when x<0 (spring is compressed) ± free-body diagram of block when x>0 (spring is extended) acceleration is back toward equilibrium position ( x=0 ) acceleration is back toward equilibrium position ( x=0 ) Simple Harmonic Motion ± a physical system that is described well by simple harmonic motion is a glider on an air-track tethered by a spring ± free-body diagram of block when x=0 (spring is in equilibrium) ± but the block can’t stop because it has velocity (Newton’s 1 st law) no acceleration
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2 Simple Harmonic Motion ± a physical system that is described well by simple harmonic motion is a glider on an air-track tethered by a spring amplitude = max | x | = A period = T = time to travel one cycle and return to original position frequency = f = 1/ T = number of cycles in a given unit of time ( units Hz = s -1 ) Energy in Simple Harmonic Motion ± no external or non-conservative forces here, so mechanical energy should be conserved ± when the block is at the maximum displacement, x=A, v=0 , ± ± Energy in Simple Harmonic Motion ± energy ‘sloshes’ between kinetic and potential Example 11.5 - Simple harmonic motion on an air track ± A spring is mounted horizontally on an air track, with the left end held stationary. We attach a spring balance to the free end of the spring, pull toward the right, and measure the elongation. A force of 6.0 N causes an elongation of 0.030 m. We remove the spring balance and attach a 0.50 kg object to the end, pulling it a distance 0.040 m. After releasing the object it oscillates in Simple Harmonic Motion. ± Find
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Chapters 11 &amp; 12 - Periodic Motion Chapters 11 &amp; 12...

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