Query 35 

course Phy 201

???????????????assignment #035

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Physics I

07-20-2007

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12:24:09

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 -->

You would take m=omega squared times k

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12:24:47

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 understand that you would use omega = sqrt(k/m), which we can solve to get m = omega^2 * k and from frequency we find angular frequency omega, using the fact that 1 complete cycle corresponds to 2 pi radians.

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12:34:48

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 -->

you could use the equation, x/L

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12:35:35

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 understand that you could use x / L Since for small angles the tension is very nearly equal to the weight mg of the pendulum this gives usTx / 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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12:35:41

Query Add comments on any surprises or insights you experienced

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12:35:45

as a result of this assignment.

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RESPONSE -->

I understand these equations.

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Good work. Let me know if you have questions. &#