course Phy 231 Dzı鐚assignment #035
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11:00:38 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 --> If we know the time of a cycle then we can find the frequency by reciprocal and have a value in units of cycles/ s, which we then convert to angular velocity by the equation of 2 'pi ( frequency) radians = a value in rad/ s = 'omega . Since 'omega = 'sqrt ( k / m), we can solve form m by 'omega^2 / k = m, and since above we found 'omega above and were given the constant, k, we can then find the mass, m, of the oscillating object.
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11:00:58 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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11:01:51 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 --> We know that k can be found by the equation of form k = m * g / L; therefore, given mass and length we can then find k.
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11:02:05 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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11:02:20 Query Add comments on any surprises or insights you experienced
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RESPONSE --> No comments
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11:02:24 as a result of this assignment.
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RESPONSE --> Ok
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11:02:29 .
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RESPONSE --> Ok
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