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the simple pendulum


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             Oscillation is a repeated periodic motion, vibration or variation in the state of an object. The time for one oscillation is called the PERIOD. The number of oscillations in a given time (usually a second) is called the FREQUENCY (vibrations per second are given the unit of the HERTZ or Hz.).
             There are three types of oscillation:.
             Free oscillation: - this is when a body oscillates with its own natural frequency. A good example of this sort of oscillation would be a large Earthquake, where the Earth is set into its natural oscillations.
             Forced oscillation: - We can make an oscillator oscillate by applying a periodic force to it. Let us make this force obey,.
             F = F0 cos w t.
             There are some transient movements, but eventually the oscillator settles down into a steady state oscillation with the frequency of the driving force. a good example would be a child on a swing.
             Damped oscillation: - In the real world, retarding forces reduce the amplitude of oscillating bodies over time. The process is called damping due to air resistance. To allow for damping, we can note that the damping force is frequently proportional to the velocity of the oscillator. .
             The time taken for a pendulum to swing backwards and forwards is almost exactly the same for each swing. In fact, the motion is so regular that for many centuries it was the most accurate means humans had of keeping track of time. A motion that repeats itself in this way is called periodic or harmonic motion. The pendulum is an example of the simplest type of harmonic motion called simple harmonic motion (SHM). Thus we see that any object that is initially displaced slightly from a stable equilibrium point will oscillate about its equilibrium position. It will, in general, experience a restoring force that depends linearly on the displacement x from equilibrium. If a body moves such that its acceleration is directly proportional to its displacement from a fixed point and is always directed towards that point, then the motion is s.


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