course Phy 201 ¹žù”“^ªûy§å®E÷ûˆ¥¥…ŒÓ¬½Ÿùÿœassignment #035
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15:28:18 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= 2 pi rad/ t=omega t= time to complete a cycle omega=sqrt of k/m solve for m
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15:34:13 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 --> ok
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15:48:42 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 --> The restoring force is releted to the weight= mass * 9.8m/s^2. For a simple pendulum, restoring force is in the same proportion to weight as displacement to length. If the displacement were .1 of the length, the restoring force would be close to .1 of the weight. The restoring force F=kx where x is the displacement from equilibrium and k is the restoring force constant Solve for k
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15:50:31 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 --> Tx=(mg/L)*x Tx is the restoring force restoring force=k*x k= mg/L Restoring force constant=mg/L
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15:51:22 Query Add comments on any surprises or insights you experienced
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RESPONSE --> Tx= the restoring force pulling the pendulum back toward equilibrium Tx= (mg/l)*x k= mg/L
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15:51:26 as a result of this assignment.
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RESPONSE -->
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15:51:31 .
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RESPONSE --> ok
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