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The position of an object connected to a spring varies with time according to the expression $x=(5.2 \mathrm{cm})$ sin $(8.0 \pi t) .$ Find (a) the period of this motion, (b) the frequency of the motion, (c) the amplitude of the motion, and (d) the first time after $t=0$ that the object reaches the position $x=2.6 \mathrm{cm} .$

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Rutgers, The State University of New Jersey

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McMaster University

give us the equation for emotion and we can say that for part A, the period T would be equaling two pi over omega. So here we would simply draw omega from the equation that they're giving us. So this would be to pie divided by 8.0 pie radiance per second, and this would be to part radiance. So this is giving us point 25 seconds for our period. Then we have for part B. The frequency is going to be the reciprocal of the period. So this would be one over 10.25 So this is giving us 4.0 hurts for part C. Then, uh, we can simply look at the equation and see that the amplitude is going to be 55.2 centimeters where we can save 0.0 52 meters. So this would be our answer for Part C and then for part D. We can say that if X is equaling 2.6 centimeters, so half of the amplitude then we can say that Omega Times t This would be equaling two arc sine of X over the amplitude A and this would be arc sine of essentially 0.5. And this is giving us 0.52 radiance and given this week and say that then T is going to be equaling 0.52 radiance divided by omega of 8.0 pie radiance per second. And so this is giving us 0.21 seconds. This would be our final answer for Part D. That is the end of the solution. Thank you for watching.

Carnegie Mellon University