phys124s11-l05

phys124s11-l05 - 1 RG, Physi cs & Ast r onomy Physi cs...

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Unformatted text preview: 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 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 =− G M r 2 r Potential energy U g =− G m 1 m 2 r Escape speed v esc = 2Gm e r 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 4 RG, Physi cs & Ast r onomy Physi cs 124, Spr i ng 2010 Basics Ladybug demos... r = r 0, = t x = r cos = r cos t r x ''Simple harmonic motion'': x = Acos t y = r sin = r sin t Focus today on one type of motion that follows a simple equation - Example: Object moves on circular path at constant speed 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 C: position at time t = 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 = − S = v / C = Acos S =− Asin 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 = d 2 x dt 2 2 x = 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 7 RG, Physi cs & Ast r onomy Physi cs 124, Spr i ng 2010 Check the answer is right......
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This note was uploaded on 03/24/2011 for the course PHYSICS 123 taught by Professor Madey during the Fall '08 term at Rutgers.

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phys124s11-l05 - 1 RG, Physi cs & Ast r onomy Physi cs...

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