course phy 121 ??[?????Z????|9w??assignment #035???????????
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14:54:39 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 --> We convert how long it takes to complete a cycle to angular frequency. I do it by finding how many cycles in one second and then multiplying by 2 pi radians. I think this is the long way, but it makes sense to me. Then I find the square root of k and divided it by omega. I square this answer to find mass. I know all of this could be simplified, but it works and I understand it.
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14:55:06 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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15:03:56 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 --> I had trouble with problem 15 which I think this one is similar to. The displace to length equaling 1/10 so restoring force being 1/10 of weight really confused me. However, when I look at the formulas I found one that fits quite nicely. k = mg/L That pretty much does it. we know mass, length and gravitational acceleration, so we can easily calculate k.
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15:08:55 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 --> I was right, but that doesn't mean much. I have some work left to do!
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15:09:41 Query Add comments on any surprises or insights you experienced
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15:09:45 as a result of this assignment.
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