Recall the demo from yesterday\'s class involving the spinning rotor, the and th
ID: 1641115 • Letter: R
Question
Recall the demo from yesterday's class involving the spinning rotor, the and their shadows. Explain the concept that this demonstration illustrated in words, then show how this understood through equations. Consider a mass on a spring undergoing forced oscillations damping. At first the oscillations are complex, meaning that the oscillation is combination of multiple In this case one of those frequencies is the natural a of the spring-mass system the other is the driving frequency (i.e. resonant frequency) of the spring-mass system the other is the driving frequency of the force. Eventually the system will settle and the oscillations will go complex to simple, with the oscillating frequency equal to the driving frequency. Consider a driven oscillator that has settled and is oscillating at the driving frequency. In general the the forced spring-mass system fluctuates the work done on the mass by the oscillating force. However compare the energy of the system at the beginning to that at the end of one will find that they are in the same. One way to see this is to note that the amplitude of the oscillations is constant. Explain why the energy of the spring-mass system at the beginning of the cycle is equal to that at the end of cycle. In particular explain why the energy is the same even though there is a force doing work throughout the For concreteness you can assume that the position of the mass and driving force are given by x = A cos wt F = F_0 cos omega t however your answer should not require any calculations.Explanation / Answer
The energy of the spring-mass system is same at the beginning of the cycle and at the end of the cycle because of the law of conservation of energy which states that energy can neither be created nor can it be destroyed, it can only be transferred. So, the sum total of energy is always constant throughout the cycle at any given point.
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