shm - Simple Harmonic Motion THEORY Vibration is the motion...

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THEORY Vibration is the motion of an object back and forth over the same ground. The most important example of vibration is simple harmonic motion (SHM). One system that manifests SHM is a mass, m, attached to a spring where k is the spring constant. Let the system reside on a horizontal table with no friction present. If the mass is pulled back a distance x from the equilibrium it will experience a spring force that obeys Hooke’s law, F = - k x. Since this is the net force on m, by Newton’s second law, -k x = m d 2 x / dt 2 OR d 2 x / dt 2 + ϖ 2 x = 0 where ϖ 2 k/m, and ϖ is called the (angular) frequency of vibration = 2 π /T, T = period =1/f, and f is the frequency . Here is the first case where we are confronted with a non-constant acceleration. The above equation is called a differential equation because it contains both a function, x(t), as well as derivatives of the function. We will solve the differential equation two ways:
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This note was uploaded on 07/29/2011 for the course PHY 2048 taught by Professor Chen during the Spring '08 term at UNF.

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shm - Simple Harmonic Motion THEORY Vibration is the motion...

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