Transcription of Exercises on Oscillations and Waves Exercise 1 - CPP
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Exercises on Oscillations and Waves Exercise 1 - CPP
Exercises on Oscillations and WavesExercise find a spring in the laboratory. When you hang 100 grams at the end of the springit stretches 10 cm. You pull the 100 gram mass 6 cm from its equilibrium position andlet it go att= 0. Find an equation for the position of the mass as a function of first find the period of the Oscillations , then we can obtain an equation forthe motion. The periodT= 2 m/k. The massmis Kg. To findk, we use thefact that 100 grams causes the spring to stretch an additional 10 cm. SinceF=k x,we havemg=k ( ) =k( )k= period of the motion is thereforeT= 2 Att= 0 themass is at its maximum distance from the origin.
f = 4 m=s This speed of 4 m/s is the initial speed for the oscillatory motion. Since the spring obeys Hooke’s law, the motion is one of simple harmonic (i.e. sinusoidal) withq != k=m= q 16=4 = 2 s 1. The general expression for simple harmonic motion is: x(t) = x 0cos(!t) + v 0! sin(!t) (10) For our example, x 0 = 0 since the blocks are at x ...
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