PHYS 211 Lecture Notes - Lecture 22: Simple Harmonic Motion, Angular Velocity
4 May 2015
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Document Summary
Total mechanical energy is conserved in simple harmonic motion, for both horizontal and vertical systems. However, because acceleration is not constant, we must use differential equations a= d(v) d (t) = d2(x) d (t ) m d2(t) d(t) The displacement of an object in simple harmonic motion behaves like a sinusoidal function, and so each progressive derivative changes the sign of the function. x (t)= asin( t)+bcos( t ) Possible solutions include x (t)= asin( t) x(t)= acos( t) *if the initial displacement is the max amplitude, the displacement equation must be in terms of cosine because the cosine graph begins at its maximum value (1). The linear displacement of an object in simple harmonic motion is equal to the angular displacement of an object moving in a circle with an angular velocity. The maximum amplitude (max. displacement from the equilibrium position)of an oscillating object is equal to the radius of the object"s respective rotational motion.
