course Phy 121 Hνassignment #035
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11:47:06 Query introductory problem set 9, #'s 12-17 How do we find the mass of a simple harmonic oscillator if we know the restoring force constant k and how long it takes to complete a cycle?
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RESPONSE --> angular frequency = sqrt(k/m). Then you would just plug in what you know.
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11:48:28 We know the basic relationship omega = sqrt(k/m), which we can solve to get m = omega^2 * k. We are given k, so if we know omega we can easily find m. We know how long it takes to complete a cycle so we can find the angular frequency omega: From the time to complete a cycle we find the frequency, which is the reciprocal of the time required. From frequency we find angular frequency omega, using the fact that 1 complete cycle corresponds to 2 pi radians.
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RESPONSE --> I can't really get the terminology correct. I thought that since we had the oscillation, we knew the angular frequency. But I see now that you have to solve for it by plugging in the oscillation into 2 pi (freqency) to get it in radians/sec.
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11:52:31 If we know the mass and length of a pendulum how can we find its restoring force constant (assuming displacements x much less than pendulum length)?
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RESPONSE --> In example 15, it said that displacement was 1/10 of the length so therefore the restoring force is 1/10 of the weight. So I am guessing that since there is the stipulation that the displacements x are much less than the pendulum length this means that this correlation applies when it is these types of problems. Then we found the k by multiply the force time displacement and then plugged it into the angular frequency equation.
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11:53:56 For small displacement from equilibrium vector resolution of the forces tells us that the x component of tension in the same proportion to tension as the displacement x to the length L: x / L Since for small angles the tension is very nearly equal to the weight mg of the pendulum this gives us Tx / m g = x / L so that Tx = (m g / L) * x. Since Tx is the restoring force tending to pull the pendulum back toward equilibrium we have restoring force = k * x for k = m g / L. So the restoring force constant is m g / L.
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RESPONSE --> ok.
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11:54:39 Query Add comments on any surprises or insights you experienced
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RESPONSE --> I am still trying to get a hang of this. The terminology is hard to remember when thinking about which equation it goes with.
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11:54:42 as a result of this assignment.
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RESPONSE -->
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