Lectures on oscillatory motion

Lectures on oscillatory motion - Periodic Motion Periodic...

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Unformatted text preview: Periodic Motion Periodic motion is motion of an object that regularly repeats The object returns to a given position after a fixed time interval Periodic motion is ubiquitous in nature and is the most important type of motion studied in physics Periodic motion A-periodic motion g Earth Notes d Sun Voyager Out of the solar system d g Sun Periodic Motion For periodic (also called oscillatory ) motion of an object to take place, forces must act on the object . Otherwise, according to the First Newtons Law, the object will move on a straight line and will never return to its initial position. aving a force acting on an object is not sufficient to induce Notes Having a force acting on an object is not sufficient to induce periodic motion, only a few special types of forces create periodic motion However, these types of motion are so wide-spread in nature that periodic motion is found everywhere Simple Harmonic Motion Consider a special kind of periodic motion for which force acting on an object is proportional to the position of the object relative to some equilibrium position The force must be in the opposite direction to the isplacement f the object from equilibrium Notes displacement of the object from equilibrium This type of force creates periodic motion which is called Simple Harmonic Motion Motion of a Spring-Mass System An example of simple harmonic motion (SHM) is a mass attached to a light spring 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 witch we will choose as the origin of our coordinate system Notes When the block is displaced from equilibrium, the spring is either stretched or compressed and thus when released will tend to return to the equilibrium un-stretched length Therefore, the spring will exert force on the block which will push it back towards equilibrium ( x=0 ) Hookes Law The magnitude of the restoring force can be is described by the Hookes Law Hookes Law states F s = - k x F s is the restoring force It is always directed toward the equilibrium position Therefore, it is always opposite the displacement from equilibrium k is the force (spring) constant x is the displacement from equilibrium position Notes More About Restoring Force The block is displaced to the right of x = 0 The position is positive The restoring force is Notes directed to the left, so it is negative F s = - k x < 0 More About Restoring Force, 2 The block is at the equilibrium position x = 0 The spring is neither tretched nor compressed Notes stretched nor compressed The force is 0, F s = More About Restoring Force, 3 The block is displaced to the left of equilibrium, so x<0 The restoring force is Notes directed to the right, so it is positive F s = - k x > 0 Acceleration...
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Lectures on oscillatory motion - Periodic Motion Periodic...

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