This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full Document
 Winter '10
 Scheibell
 Force, Simple Harmonic Motion

Click to edit the document details