The outlines of physics: an elementary text-book . rmine to the nearest second the timerequired for one hundred oscillations. Repeat the observation at leastfive times and average the results. (6) Mount the pendulum at 45°, as shown in Fig. 32, and thusresolve g into two equal components, a and 6, only one of which, thecomponent a, tends to produce oscillation. The component a is to i? as 7 : 10, nearly (more accurately 7-07 to10). It is the object of the observation to verify the fact that the 44 THE OUTLINES OF PHYSICS square of the rate of the pendulum in this new position bears theabove ra
The outlines of physics: an elementary text-book . rmine to the nearest second the timerequired for one hundred oscillations. Repeat the observation at leastfive times and average the results. (6) Mount the pendulum at 45°, as shown in Fig. 32, and thusresolve g into two equal components, a and 6, only one of which, thecomponent a, tends to produce oscillation. The component a is to i? as 7 : 10, nearly (more accurately 7-07 to10). It is the object of the observation to verify the fact that the 44 THE OUTLINES OF PHYSICS square of the rate of the pendulum in this new position bears theabove ratio to the square of its rate when mounted relation between force and period is as follows: ,2(2 ^ in which the period under action of the force corresponding to g isdesignated by tg, and the period ^ under the action of a, by <„. Thelaw may be stated thus: The square of the rate of a pendulum is proportional to the force towhich its oscillations are due. (c) Verify the law for an angle of 60° (at this inclination a = ig). 1. Fig. 32. 1 The general relation of gr to a is expressed in the formulaa = gcosa,where a is the angle which the line joining centers of suspension and ofoscillation makes with the vertical line through the former. THE SIMPLE PENDULUM 45 42. Summary of the Results of Experiments 5, 6, and 7. (1) The period of oscillation of a simple pendulum isindependent of the material of which the bob is made, andalso of the mass of the bob. (2) The square of the period of oscillation is propor-tional to the length of the pendulum. (3) The period is approximately independent of theamplitude of oscillation. (4) The square of the period of oscillation is inversely-proportional to the force to which the oscillations are due. These results may be gathered into a formula whichstates what is generally called the law of the simplependulum, viz.: In this expression t is the period in seconds; I is thelength in centimeters; g is the acceleration due to the fo
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