# Ch-13 - Chapter 13 Vibrations and Waves Hooke's Law Fs = k...

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Chapter 13 Vibrations and Waves

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Hooke’s Law F s = - k x F s is the spring force k is the spring constant It is a measure of the stiffness of the spring A large k indicates a stiff spring and a small k indicates a soft spring x is the displacement of the object from its equilibrium position x = 0 at the equilibrium position The negative sign indicates that the force is always directed opposite to the displacement
Hooke’s Law Applied to a Spring – Mass System When x is positive (to the right), F is negative (to the left) When x = 0 (at equilibrium), F is 0 When x is negative (to the left), F is positive (to the right)

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Simple Harmonic Motion Motion that occurs when the net force along the direction of motion obeys Hooke’s Law The force is proportional to the displacement and always directed toward the equilibrium position The motion of a spring mass system is an example of Simple Harmonic Motion Not all periodic motion over the same path can be considered Simple Harmonic motion To be Simple Harmonic motion, the force needs to obey Hooke’s Law
Amplitude Amplitude, A The amplitude is the maximum position of the object relative to the equilibrium position In the absence of friction, an object in simple harmonic motion will oscillate between the positions x = ±A

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Period and Frequency The period, T, is the time that it takes for the object to complete one complete cycle of motion From x = A to x = - A and back to x = A The frequency, ƒ, is the number of complete cycles or vibrations per unit time ƒ = 1 / T Frequency is the reciprocal of the period
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Ch-13 - Chapter 13 Vibrations and Waves Hooke's Law Fs = k...

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