Physcis Lab 1 - Objective The functional relationship...

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Objective: The functional relationship between the period of vibration of a ring and its diameter will be determined. Introduction If a ring which is initially hanging at rest from a knife edge is displaced from its equilibrium position and then released, it will oscillate about its equilibrium position. These oscillations will have a characteristic time interval called the period (T), which is the time taken for one complete cycle of oscillation of the ring. The period can be determined by measuring the time it takes for the ring to pass through its equilibrium (or some other) position in its swing to when it next passes through that position moving in the same direction as before. In this experiment the periods of vibration of several rings having different diameters will be measured. It will be observed that the periods are different for the rings with different diameters, showing the period and diameter to be related parameters. The objective of this
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experiment is to determine the functional relationship between the period of vibration of a ring and its diameter. Experience shows that the functional dependence between two related parameters frequently has the form of a power law . If this turns out to be true for the vibrating ring, then the period will be proportional to some power (p) of the diameter (D) and we can write: T = KD P ……………………………………….……...1) T = the period k = the constant of proportionality (to be determined) D = the diameter p = some power to be determined where k is a constant of proportionality. Assuming the power law does indeed hold true, our task is now to determine the numerical values of the constants k and p in equation 1). Since T is directly proportional to D p , a graph of T – vs – D will not yield a straight line (unless, be chance, p=1). However, if a smooth curve were to be drawn through the data points, then the slope of this curve would decrease as D increases is p<1, whereas the slope would increase with increasing D if p>1. Therefore, by observing how the slope of the T – vs – D
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