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Chapter 13

Chapter 13. Oscillations About Equilibrium (Cont.). Outline. Energy conservation in oscillatory motion The simple pendulum The period of a simple pendulum Driven oscillations and resonance. Energy conservation in oscillatory motion.

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Chapter 13

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  1. Chapter 13 Oscillations About Equilibrium (Cont.) Dr. Jie Zou PHY 1151G Department of Physics

  2. Outline • Energy conservation in oscillatory motion • The simple pendulum • The period of a simple pendulum • Driven oscillations and resonance Dr. Jie Zou PHY 1151G Department of Physics

  3. Energy conservation in oscillatory motion • In an ideal system with no friction or other nonconservative forces, the total energy (E) is conserved. • For a mass on a horizontal spring: • Total energy E = K + U • K = kinetic energy = (1/2)mv2 • U = elastic potential energy = (1/2)kx2 • The kinetic (K) and potential (U) energy change with time, but the total energy E is conserved. • It can be shown that E = (1/2)kA2, where A is the amplitude of oscillation. Dr. Jie Zou PHY 1151G Department of Physics

  4. Energy vs. position in simple harmonic motion Dr. Jie Zou PHY 1151G Department of Physics

  5. Example • A 0.980-kg block slides on a frictionless, horizontal surface with a speed of 1.32 m/s. The block encounters an unstretched spring with a force constant of 245 N/m. • (a) How far is the spring compressed before the block comes to rest? • (b) How long is the block in contact with the spring before it comes to rest? • Answers: (a) 0.0835 m (b) 0.0993 s Dr. Jie Zou PHY 1151G Department of Physics

  6. The pendulum • Simple pendulum: consists of a mass m suspended by a light string or rod of length L. • Period of a pendulum: • The period of a simple pendulum depends on the length of the pendulum and the acceleration of gravity. It is independent of the mass and the amplitude. L m Dr. Jie Zou PHY 1151G Department of Physics

  7. Example • A pendulum is constructed from a string 0.627 m long attached to a mass of 0.250 kg. The pendulum completes one oscillation every 1.59 s. Find the acceleration of gravity, g. • “Gravity maps” are valuable tools for geologists attempting to understand the underground properties of a given region, such as density of rocks. Dr. Jie Zou PHY 1151G Department of Physics

  8. Driven oscillations and resonance • Natural frequency, f0: The frequency at which the system oscillates when it is not driven. • In general, driving any system at a frequency near its natural frequency results in large oscillations. • Resonance: This type of large response, due to frequency matching, is known as resonance. Tacoma Narrows bridge, 1940 Dr. Jie Zou PHY 1151G Department of Physics

  9. Homework • See online homework on www.masteringphysics.com Dr. Jie Zou PHY 1151G Department of Physics

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