Lectures on oscillatory motion

# Lectures on oscillatory motion - Periodic Motion •...

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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 Newton’s 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 ) Hooke’s Law • The magnitude of the restoring force can be is described by the Hooke’s Law • Hooke’s 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 •...

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