query assignment 35

course phy201

y̡Ą}v|]~Uassignment #035

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

`p򿰜yԊo

Physics I

12-03-2007

......!!!!!!!!...................................

12:11:36

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?

......!!!!!!!!...................................

RESPONSE -->

Know k and T

Want to know m

T = 2pi* sqrt of (m/k)

so

(T/2pi)^2 * k = m

.................................................

......!!!!!!!!...................................

12:13:51

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.

......!!!!!!!!...................................

RESPONSE -->

why do we say angular frequency instead of angular velocity like we did when studying circular motion?

This is confusing to me. Whenever I hear the word frequency i think of the the reciprocal expressed in cycles / sec.

In SHM nothing is actually moving around the reference circle, so nothing actually has an angular velocity.

Frequency is measured in cycles per second. Whatever the angular velocity of the reference circle, it translates into a certain number of radians per second (a cycle is 2 pi radians, so a cycle per second is 2 pi rad / s), radian being a specific measure of angle. So cycles / sec is frequency, rad / sec is angular frequency. To get angular frequency we multiply frequency in cycles / sec by 2 pi rad / cycle.

Angular frequency is the frequency with which the phase angle (i.e., the reference-circle angle) changes.

.................................................

......!!!!!!!!...................................

12:20:22

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)?

......!!!!!!!!...................................

RESPONSE -->

k = mg/L

.................................................

......!!!!!!!!...................................

12:20:39

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.

......!!!!!!!!...................................

RESPONSE -->

ok

.................................................

......!!!!!!!!...................................

12:21:11

Query Add comments on any surprises or insights you experienced

......!!!!!!!!...................................

RESPONSE -->

still need to work more SHM problems to become fully comfortable.

It takes awhile; the calculus might be useful to you , since you know it. x(t) = A cos(omega * t) or A sin(omega * t); the velocity is v(t) = x ' (t) and the acceleration is a(t) = x '' ( t) = v ' (t). With each derivative the chain rule gives you a factor of omega.

.................................................

......!!!!!!!!...................................

12:21:22

.

......!!!!!!!!...................................

RESPONSE -->

ok

Enter, as appropriate, an answer to the question, a critique of your answer in response to a given answer, your insights regarding the situation at this point, notes to yourself, or just an OK.

Always critique your solutions by describing any insights you had or errors you makde, and by explaining how you can make use of the insight or how you now know how to avoid certain errors. Also pose for the instructor any question or questions that you have related to the problem or series of problems.

.................................................

&#

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