Lecture 34

Lecture 34 - Last Meeting Physics 231 General University...

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1 Physics 231 General University Physics Lecture 34 Lecture 9 1 Last Meeting ± Oscillatory Motion ² Kinematics Lecture 9 2 Today ± Oscillatory Motion ² Energy ² Damped Oscillations ² Forced Oscillations ² Resonance Lecture 9 3 Test 3 average = 63 ± Letter grade based on the 3 tests ± 78 ----> A ± 65 – 78 ----> B ± 50 – 65 ----> C ± 42 – 50 ----> D ± 42 ----> E Histogram 0 5 10 15 20 25 30 35 0 20 40 60 80 100 Bin Frequency Frequency Lecture 9 4 Kinematics of SHM 2 2 2 () cos ( ) sin( t ) cos( t ) x tA t dx vA dt dx aA dt ω φ ωω ωφ =+ == + + Lecture 9 5 Energy of the SHM Oscillator ± Kinetic energy ² K = ½ mv 2 = ½ m 2 A 2 sin 2 ( t + ) ± Elastic potential energy ² U = ½ kx 2 = ½ kA 2 cos 2 ( t + ) ± Total mechanical energy ² is proportional to the square of the amplitudes ² E= K + U = ½ kA 2 ² is constant
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2 Lecture 9 6 Energy of the SHM Oscillator (cont.) ± Energy is continuously being transferred between potential energy stored in the spring and the kinetic energy of the block ± Energy can be used to find the velocity () 22 22 2 k vA x m Ax ω 2 max 2 max 2 1 2 1 mv kx E = = Lecture 9 7 Conservation of Mechanical Energy ± Energy is transformed between potential energy but the total mechanical energy does not change. Lecture 9 8 Lecture 9 9 Energy in SHM Lecture 9 10 (Simple) Pendulum ± Demo: Large Pendulum ² Restoring force; Equilibrium ± LD: (CC1B33) Sand Pendulum ± The force acting on the bob are T and m g ² T is the tension force exerted on the bob by the string ² m g is the gravitational force Lecture 9 11 (Simple) Pendulum ± Tangential component ± But s= θ
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This note was uploaded on 11/16/2010 for the course PHY 231 taught by Professor Ellis during the Spring '08 term at Kentucky.

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Lecture 34 - Last Meeting Physics 231 General University...

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