# Demo11 - Demonstrations for Class 11 Mechanical Oscillations Most small mechanical oscillations can be approximated as simple harmonic oscillations

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Demonstrations for Class 11 --- Mechanical Oscillations Most small mechanical oscillations can be approximated as simple harmonic oscillations and can be modeled as a spring. You remember that for a spring, the restoring force is kx F - = , where k is known as the "restoring constant". The force is directly proportional to how far you stretch the spring. That lets it be simple harmonic. Simple harmonic oscillations are described by a differential equation. For a spring and mass, neglecting friction and gravity, 0 d d 2 2 = + x m k t x , and the solution for x is a sinusoid, ) cos( φ ϖ + = t A x , where A is the maximum displacement, or the Amplitude, is the angular frequency, and is a phase offset called the phase constant. The total energy for an oscillating mass is simply the sum of its potential energy at any time (from compressing or extending the spring) and its kinetic energy at any time (from the motion of the mass itself): 2 2 2 1 2 1 kx mv E + = . Taking

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## This note was uploaded on 09/17/2008 for the course PHYS 1200 taught by Professor Stoler during the Spring '06 term at Rensselaer Polytechnic Institute.

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Demo11 - Demonstrations for Class 11 Mechanical Oscillations Most small mechanical oscillations can be approximated as simple harmonic oscillations

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