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phys124s11-l05 - Physi cs 124 Spr i ng 2010 Physics 124...

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1 RG, Physi cs & Ast r onomy Physi cs 124, Spr i ng 2010 Physics 124, Spring 2010 Class web pages: http://www.physics.rutgers.edu/ugrad/124 Exam next Monday Feb 21 9:40-11:00 PM. Covers everything up through gravity / last week One cheat sheet allowed (both sides). ARC 103: sections 04, 05, 07, 08, 09, 12, 16, 19 HILL 114: sections 01, 02, 03, 15, 18 SEC 111: sections 06, 10, 11, 13, 14 Email Profs. Gershenson ([email protected]) “immediately” if you need makeup. Those taking makeup will be given coordinates by email. Use gradebook section
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2 RG, Physi cs & Ast r onomy Physi cs 124, Spr i ng 2010 Lecture 4 Summary Today: periodic motion / oscillations / waves F 1 on 2 =− G m 1 m 2 | r 12 | 2 r 12 = m 1 g Kepler's 1 st law : elliptical orbits with the sun at one focus. Kepler's 2 nd law : orbit sweeps out equal areas in equal times Kepler's 3 rd law : T 2 a 3 = constant = 4 2 Gm sun Gravitational field g = F g m =− GM r 2 r Potential energy U g =− G m 1 m 2 r Escape speed v esc = 2Gm e r
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3 RG, Physi cs & Ast r onomy Physi cs 124, Spr i ng 2010 Basics Repeating motion, Ideally constant period Ideally undamped – no energy lost (for most of class) Examples: waves in ocean strings in piano light waves molecular vibration mass on a spring Pendulum x-component of circular motion chainfall Computer demo... There are many types of repeating motion
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4 RG, Physi cs & Ast r onomy Physi cs 124, Spr i ng 2010 Basics Ladybug demos... r = r 0,  =  t x = r 0 cos  = r 0 cos t  r x ''Simple harmonic motion'': x = Acos  t  y = r 0 sin  = r 0 sin t Focus today on one type of motion that follows a simple equation - Example : Object moves on circular path at constant speed
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5 RG, Physi cs & Ast r onomy Physi cs 124, Spr i ng 2010 Two equations: sometimes one is more convenient than other or Why not just the simple x = Acos t A: amplitude of motion r 0 C : position at time t = 0 r x ''Simple harmonic motion'': x = Acos  t  Sometimes we start our clock at the wrong time x = Ccos t Ssin t : angular frequency of motion 2 / T T : period of motion time it takes to repeat S: related to velocity at time t = 0 S = v / C = Acos S =− Asin
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6 RG, Physi cs & Ast r onomy Physi cs 124, Spr i ng 2010 Mass on a Spring F = ma =− kx m d 2 x dt 2 kx = 0 d 2 x dt 2  2 x = 0 rest position x with 2 = k / m m k Hooke's law: F = − kx k: spring constant Force towards rest position Force displacement Best way to solve differential equation: know the answer x = Acos  t  A: amplitude : angular frequency : phase shift Usual approximation: massless spring
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7 RG, Physi cs & Ast r onomy Physi cs 124, Spr i ng 2010 Check the answer is right... d 2 x dt 2  2 x = 0  − 2 Acos  t  2 Acos  t  = 0 Best way to solve differential equation: know the answer x = Acos  t  dx dt = − Asin  t  d 2 x dt 2 = − 2 Acos  t 
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8 RG, Physi cs & Ast r onomy Physi cs 124, Spr i ng 2010 Mass on a Spring
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