query 35

course phy 201

2 8/2

If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

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:

mass = omega ^2 * k

f = 1/T

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

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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:

Tx = (m g / L) * x.

restoring force = k * x

for k = m g / L

--> restoring force constant is m g / L.

confidence rating: 3

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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.

STUDENT COMMENT:

I don’t see the relevance of this to much…what benefit is knowing this towards a total

understanding of pendulums?

INSTRUCTOR RESPONSE:

This tells you the net force on the pendulum mass as a function of position, and justifies our assumption that the pendulum undergoes simple harmonic motion.

In other words, this is the very first thing we need to know in order to analyze the pendulum.

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Self-critique (if necessary): ok

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Self-critique Rating: ok

&#This looks good. Let me know if you have any questions. &#