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Simple Harmonic Motio1

Simple Harmonic Motio1 - always given by F x = kx where the...

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Simple Harmonic Motion Having established the basics of oscillations, we now turn to the special case of simple harmonic motion. We will describe the conditions of a simple harmonic oscillator, derive its resultant motion, and finally derive the energy of such a system. The Simple Harmonic Oscillator Of all the different types of oscillating systems, the simplest, mathematically speaking, is that of harmonic oscillations. The motion of such systems can be described using sine and cosine functions, as we shall derive later. For now, however, we simply define simple harmonic motion, and describe the force involved in such oscillation. To develop the idea of a harmonic oscillator we will use the most common example of harmonic oscillation: a mass on a spring. For a given spring with constant k , the spring always puts a force on the mass to return it to the equilibrium position. Recall also that the magnitude of this force is
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Unformatted text preview: always given by: F ( x ) = - kx where the equilibrium point is denoted by x = 0 . In other words, the more the spring is stretched or compressed, the harder the spring pushes to return the block to its equilibrium position. This equation is only valid if there are no other forces acting on the block. If there is friction between the block and the ground, or air resistance, the motion is not simple harmonic, and the force on the block cannot be described by the above equation. Though the spring is the most common example of simple harmonic motion, a pendulum can be approximated by simple harmonic motion, and the torsional oscillator obeys simple harmonic motion. Both of these examples will be examined in depth in Applications of Simple Harmonic Motion ....
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