Asst_35_query

course Phy 121

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assignment #035

ŝInUᾗWʙw

Physics I

07-28-2006

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18:26:05

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 must first multiply 2pi radians by the time to get the number of radians per second it takes to complete the cycle.

we take the square of this figure and divide by the restoring force constant to find the mass.

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18:26:32

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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18:30:18

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 find the weight of the pendulum - mass * 9.8 m/s^2

the relaion ship between the length and displacent will be similar to that of the force and the weight. which is how we calculate the restoring force.

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18:30:51

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 -->

m g / L

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18:30:54

Query Add comments on any surprises or insights you experienced

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RESPONSE -->

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18:30:56

as a result of this assignment.

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Good work. Let me know if you have questions.