Query 35

course phy201

UїOBЬassignment #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.

yXVH

Physics I

06-01-2007

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

13:43:48

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 -->

Solve `omega=`sqrt(k/m) for m=k/`omega^2. f=1/T. f*2`pi=`omega.

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

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

13:46:41

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 -->

I think you might have made an algebra error: `omega=`sqrt(k/m) `omega^2=k/m. m`omega^2=k. m=k/`omega^2.

You're right.

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

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

13:48:57

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 -->

As obtained earlier: k=mg/L

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

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

13:49:02

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

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

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

13:50:26

Query Add comments on any surprises or insights you experienced

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

RESPONSE -->

Just good reinforcement for my SHM problem solving skills.

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

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

13:50:29

as a result of this assignment.

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

RESPONSE -->

.

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

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

13:50:32

.

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

RESPONSE -->

.

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

"

Very good. Let me know if you have questions.