# PHYS102Lec4 - Chapter 13 Vibrations and Waves Dr Armen...

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Chapter 13 Vibrations and Waves Dr. Armen Kocharian

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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 Force The force always acts toward the equilibrium position It is called the restoring force The direction of the restoring force is such that the object is being either pushed or pulled toward the equilibrium position

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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) Please replace with active fig. 13.1
Motion of the Spring-Mass System Assume the object is initially pulled to a distance A and released from rest As the object moves toward the equilibrium position, F and a decrease, but v increases At x = 0, F and a are zero, but v is a maximum The object’s momentum causes it to overshoot the equilibrium position

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Motion of the Spring-Mass System, cont The force and acceleration start to increase in the opposite direction and velocity decreases The motion momentarily comes to a stop at x = - A It then accelerates back toward the equilibrium position The motion continues indefinitely
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

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Simple Harmonic Motion, cont. 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
Acceleration of an Object in Simple Harmonic Motion Newton’s second law will relate force and acceleration The force is given by Hooke’s Law F = - k x = m a a = -kx / m The acceleration is a function of position Acceleration is not constant and therefore the uniformly accelerated motion equation cannot be applied

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Elastic Potential Energy A compressed spring has potential energy
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PHYS102Lec4 - Chapter 13 Vibrations and Waves Dr Armen...

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