35 Query

course Phy 201

7/27 5:45PM

035. `query 35

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Question: `qQuery 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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Your solution:

If we want to find frequency, we first need to find the time it takes to finish one cycle. This is found by using omega and the change in position. Omega here will equatl sqroot(k/m). We have k in the situation we can solve for m by using omega^2/k=m. Then we can this to find time. Frequency is equal to 1/t so 2pi/omega=time. 1/t= freq

confidence rating: 3

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Given Solution:

`aWe 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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Self-critique (if necessary): OK

Self-critique Rating: OK

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Question: `q 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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Your solution:

Tension at x will be equal to (mg/L)*x

We know that F=k(x) so we have F=k(T/mg/L)

T and F should be equal so solving for k we will get k=mg/L

confidence rating: 2

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Given Solution:

`aFor 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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Self-critique (if necessary):

OK

Self-critique Rating: OK

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Question: `q Query Add comments on any surprises or insights you experienced as a result of this assignment.

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Self-critique (if necessary):

It is nice to figure out a lot of the formulas we are using since they are so new. I am slowely figuring most of them out at this point.

Self-critique Rating:

OK

&#Very good work. Let me know if you have questions. &#