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Chapter VII Periodic Motions

Chapter VII Periodic Motions. Periodic Motion Simple Harmonic Motion Energy of The Simple Harmonic Oscillator Simple Pendulum. A. Periodic Motion.

yvonne-scott
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Chapter VII Periodic Motions

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  1. Chapter VIIPeriodic Motions • Periodic Motion • Simple Harmonic Motion • Energy of TheSimple Harmonic Oscillator • Simple Pendulum

  2. A. Periodic Motion The amplitude of the motion, denoted by A, is the maximum magnitude of displacement from equilibrium-that is, the maximum value of Ixl. It is always positive.

  3. A complete vibration, or cycle, is one complete round tripsay, from A to -A and back to A, or from 0 to A, back through 0 to -A, and back to O. • The period, T, is the time for one cycle. It is always positive. The SI unit is thesecond, but it is sometimes expressed as "seconds per cycle." • The frequency, f, is the number of cycles in a unit of time. It is always positive. The SI unit of frequency is the hertz. 1 hertz = I Hz = 1 cycle/s = 1 S-l The angular frequency (rad/s), , is 2 times the frequency (cycle/s): = 2 f The number 2 as having units rad/cycle.

  4. B. Simple Harmonic Motion The minus sign means the acceleration and displacemem always have oppositesigns. • = phase angle • (t + ) = Phase

  5. The frequency and period depend only on the mass of the block andon the force constant of the spring

  6. C. Energy of The Simple Harmonic Oscillator • The total mechanical energy of a simple harmonic oscillator is a constant of the motion and is proportional to the square of the amplitude. • Note, that U is small when K is large, and vice versa, because the sum must be constant.

  7. D. Simple Pendulum x

  8. The period and frequency of a simple pendulum depend onlyon the length of the string and the acceleration due to gravity. • Because theperiod is independent of the mass, we conclude that all simple pendulums that areof equal length and are at the same location (so that g is constant) oscillate withthe same period.

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