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First time is the lat time. ...Wisdom

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 Author Topic: about Simple harmonic motion...  (Read 16279 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
kennethkyho
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 « Embed this message on: December 15, 2008, 09:09:59 pm »

in my knowledge,
there are two kinds of simple harmonic motion...

one is simple pendulum, the other is spring oscillation...

and one in school,
i was doing experiment of spring oscillation...

a light spring was hang on a retort stand and a slotted mas was suspended with hanger from it.
and the mass started oscillating vertically with a small displacement.
and i need to court the period of the 50 oscillations.
then i just repeat the timing with different mass.
and finally i need to find the force constant and effective mass of the spring.

here's the question...
when the mass is too small and the amplitude is large, the mass oscillated like a simple pendulum instead of oscillating vertically.
why
also, is there any relationship between the period of the spring oscillating vertically and the period of the "simple pendulum"

Thanks..
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lookang
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http://weelookang.blogspot.com

 « Embed this message Reply #1 on: December 16, 2008, 08:10:28 am » posted from:Singapore,,Singapore

Applets on the 2 kind of SHM are on the forum, "search" the entire forum or just the EJS boards usually gives the applets I am looking for.

simple harmonic motion: simple pendulum
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=818.msg3092#msg3092
http://www.phy.ntnu.edu.tw/ntnujava/index.php?action=dlattach;topic=818.0;attach=470

simple harmonic motion:spring oscillation
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=349.0

when the mass is too small and the amplitude is large, the mass oscillated like a simple pendulum instead of oscillating vertically.
why
I  think it is due to the 3-D ( x , y and z) translational degree of freedoms and the rotational degree of freedom cause the vertical pendulum to swing in all possible ways in additional to the up and down you set it to move in SHM. The reason is there may be a slight displacement "off" the line of action of the spring.

also, is there any relationship between the period of the spring oscillating vertically and the period of the "simple pendulum"
vertical spring formula is T = 2*Math.PI.Math.sqrt(k/m) valid for F = kx hooke's law only.
picture taken from http://dev.physicslab.org/img/72f3a800-5564-428e-97e2-fb76f4cbef80.gif
swing pendulum formula is T = 2*Math.PI.Math.sqrt(L/g) valid for small oscillations only.
picture taken from http://www.school-for-champions.com/science/images/pendulum_equations-factors.gif
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kennethkyho
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 « Embed this message Reply #2 on: December 16, 2008, 07:41:08 pm »

Sorry...

I think u misunderstand that the vertical spring should be up-side-down...
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lookang
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http://weelookang.blogspot.com

 « Embed this message Reply #3 on: December 16, 2008, 08:17:16 pm »

fundamentally the equations to model the spring mass system motion vertically is the same.

F = ma

k*x = m*a

i just couldn't find the mass at the bottom picture.

you could redesign the java applet from Prof hwang to suit your graphics
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Fu-Kwun Hwang
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 « Embed this message Reply #4 on: December 16, 2008, 11:50:28 pm »

Please check out Spring + Pendulum
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