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Unformatted text preview: Chapter 12 Oscillatory/Periodic Motion Mass on a spring harmonic oscillation damped oscillation forced oscillation Pendulum point mass on a string extended object on a string A classic example of elastic deformation is given by springs: When the force is removed, they return to their original shape, length. Elastic deformation: another form of potential energy Hooke’s Law The spring must exert an upward force on you to balance gravity. When you step on a spring, it contracts. When it contracts (or expands), it acts to oppose this deformation according to the equation where x is the amount by which the spring is squeezed or stretched from its equilibrium length . Hooke’s Law The spring must exert an upward force on you to balance gravity. When you step on a spring, it contracts. When it contracts (or expands), it acts to oppose this deformation according to the equation where x is the amount by which the spring is squeezed or stretched from its equilibrium length . More About Restoring Force • The block is displaced to the right of x = 0 – The position is positive • The restoring force is directed to the left More About Restoring Force • The block is at the equilibrium position – x = 0 • The spring is neither stretched nor compressed • The force is 0 More About Restoring Force • The block is displaced to the left of x = 0 – The position is negative • The restoring force is directed to the right Motion of a SpringMass System • A block of mass m is attached to a spring, the block is free to move on a frictionless horizontal surface • When the spring is neither stretched nor compressed, the block is at the equilibrium position – x = 0 Periodic Motion • Periodic motion is motion of an object that regularly repeats – The object returns to a given position after a fixed time interval • A special kind of periodic motion occurs in mechanical systems when the force acting on the object is proportional to the position of the object relative to some equilibrium position Acceleration • The force described by Hooke’s Law is the net force in Newton’s Second Law Acceleration • The acceleration is proportional to the displacement of the block • The direction of the acceleration is opposite the direction of the displacement from equilibrium • An object moves with simple harmonic motion whenever its acceleration is proportional to its position (away from equilibrium) and is oppositely directed to the displacement from equilibrium Acceleration • The acceleration is not constant – Therefore, the kinematic equations we learned in 6A cannot be applied – If the block is released from some position x = A , then the initial acceleration is – kA / m • Its speed is zero – When the block passes through the equilibrium position, a = 0 • Its speed is a maximum – The block continues to x =  A where its acceleration is + kA / m Motion of the Block • The block continues to oscillate between – A and + A – These are turning points of the motion...
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This note was uploaded on 02/03/2010 for the course NEUROSCI 101A taught by Professor Scheibell during the Winter '10 term at UCLA.
 Winter '10
 Scheibell

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