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$\bullet$ $\bullet$ An object of unknown mass is attached to an ideal spring with force constant 120 $\mathrm{N} / \mathrm{m}$ and is found to vibrate with a frequency of 6.00 $\mathrm{Hz}$ . Find (a) the period, (b) the angular frequency, and (c) the mass of this object.
0.167 $\mathrm{s}$37.7 $\mathrm{rad} / \mathrm{s}$0.0844 $\mathrm{kg}$
Physics 101 Mechanics
Chapter 11
Elasticity and Periodic Motion
Equilibrium and Elasticity
Periodic Motion
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in this problem, we're going to need the following three formulas in the first relates the two different types of frequencies. A second relates the annual frequency to the spring concert in the Mass, and the third is just the period in terms of the regular frequency in part A. We want to figure out what the period is, and we know the frequency. And so we can use this equation. And like in what our neural frequency is, which is six hertz, this gives a 0.167 seconds, which is the period in part B. We want to know what the angular frequency is, and we know the frequency. And so we can use this equation here to salt, for they were frequency. It's equal to two pi f. We're F. It is six hertz and so the angler frequent scenes of being 37.7 radiance per second. And that's the answer to part. Me and Marci were going to use this formula, except I'm going to solve for the mass. Let's offer them asked like it okay over Omega squared. And then the problem gets us K. And we just calculate what Omega wass, and so this is equal to 1 20 over 37 0.7 squared, which is equal to 0.8 44 kilograms, and that's the problem.
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