| Topic: |
Science > Physics |
| User: |
"Freiddy" |
| Date: |
22 Feb 2007 01:54:18 PM |
| Object: |
Wired Pendulum |
I am unable to prove a certain equation for a special pendulum.
The pendulum is a sharply bent wire like a upside down "V" with an
angle of Theta. V is hanged onto a pin and allowed to vibrate
slightly. The entire length is L and g is 9.8 N/kg. The period T of
the oscillation is given implicitly by:
T^4=1 / (X cos(theta) + X)
X is a constant of L, g & pi.
I think I made a mistake while finding the center of mass of the wire.
Then I may be able use the T=2pi sqrt(l/g) approximation to find the
period.
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| User: "Alois Steindl" |
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| Title: Re: Wired Pendulum |
23 Feb 2007 01:52:20 AM |
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"Freiddy" <fei.yuanbw@gmail.com> writes:
I am unable to prove a certain equation for a special pendulum.
The pendulum is a sharply bent wire like a upside down "V" with an
angle of Theta. V is hanged onto a pin and allowed to vibrate
slightly. The entire length is L and g is 9.8 N/kg. The period T of
the oscillation is given implicitly by:
T^4=1 / (X cos(theta) + X)
X is a constant of L, g & pi.
I think I made a mistake while finding the center of mass of the wire.
Then I may be able use the T=2pi sqrt(l/g) approximation to find the
period.
Hello "Freiddy",
your equation looks completely wrong.
I suggest you first intensively consult a treatment of a "physical pendulum"
(i.e. a pendulum, which has mass and rotatory inertia; contrary to a
mathematical pendulum, which is just a mass point at the end of a
massless string). After that you calculate these quantities for your
model and use the angle between the vertical and the line connecting
the fixed point and the center of mass as degree of freedom.
Alois
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| User: "Freiddy" |
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| Title: Re: Wired Pendulum |
24 Feb 2007 05:38:40 AM |
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No, the equation is mostly likely correct (I'm not the one who derived
this). But the method of derivation is what I require currently.
Freiddy
http://fei.yuanbw.googlepages.com/
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| User: "" |
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| Title: Re: Wired Pendulum |
24 Feb 2007 07:44:52 AM |
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On Feb 22, 7:54 pm, "Freiddy" <fei.yua...@gmail.com> wrote:
I am unable to prove a certain equation for a special pendulum.
The pendulum is a sharply bent wire like a upside down "V" with an
angle of Theta. V is hanged onto a pin and allowed to vibrate
slightly. The entire length is L and g is 9.8 N/kg. The period T of
the oscillation is given implicitly by:
T^4=1 / (X cos(theta) + X)
X is a constant of L, g & pi.
I think I made a mistake while finding the center of mass of the wire.
Then I may be able use the T=2pi sqrt(l/g) approximation to find the
period.
Well, I got the answer given. I'm no expert with this stuff so it
might have been just luck. But if it's of any help then if you post
what you've done I can tell you where your derivation deviates from
mine. (Btw, I didn't anywhere calculate centre of mass... I did it by
calculating torque, moment of inertia and angular acceleration.)
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| User: "Freiddy" |
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| Title: Re: Wired Pendulum |
24 Feb 2007 01:02:00 PM |
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Okay, I'll tell you.
The actual formula of X is
X = 1/2 (3g^2 / (4 * pi^2 * L^2))^2
Did you get that? (If there is any slight deviations, such as
different powers, then maybe I'm wrong, since I kinda forgot the
formula)
Freiddy
http://fei.yuanbw.googlepages.com/
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| User: "" |
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| Title: Re: Wired Pendulum |
24 Feb 2007 01:34:17 PM |
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On Feb 24, 7:02 pm, "Freiddy" <fei.yua...@gmail.com> wrote:
Okay, I'll tell you.
The actual formula of X is
X = 1/2 (3g^2 / (4 * pi^2 * L^2))^2
Did you get that? (If there is any slight deviations, such as
different powers, then maybe I'm wrong, since I kinda forgot the
formula)
Freiddyhttp://fei.yuanbw.googlepages.com/
Close, but not quite. I got
X = 1/2 * (3*g / (4*pi^2*L))^2
I didn't check what I was doing particularly carefully though, so it's
possible I may have goofed. I thought the powers of L and g in my
answer looked plausible-ish though, as they agree with the simple
pendulum case.
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| User: "Freiddy" |
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| Title: Re: Wired Pendulum |
26 Feb 2007 03:29:34 PM |
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On Feb 24, 9:34 pm, wrote:
On Feb 24, 7:02 pm, "Freiddy" <fei.yua...@gmail.com> wrote:
Okay, I'll tell you.
The actual formula of X is
X = 1/2 (3g^2 / (4 * pi^2 * L^2))^2
Did you get that? (If there is any slight deviations, such as
different powers, then maybe I'm wrong, since I kinda forgot the
formula)
Freiddyhttp://fei.yuanbw.googlepages.com/
Close, but not quite. I got
X = 1/2 * (3*g / (4*pi^2*L))^2
I didn't check what I was doing particularly carefully though, so it's
possible I may have goofed. I thought the powers of L and g in my
answer looked plausible-ish though, as they agree with the simple
pendulum case.
I think it's right. Remember,I forgot the exact formula.
Freiddy
http://fei.yuanbw.googlepages.com/
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| User: "Freiddy" |
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| Title: Re: Wired Pendulum |
27 Feb 2007 01:59:18 PM |
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So could you please show how you found the answer? Thanks. It doesn't
need to be very detailed, some explanation would be enough.
Freiddy
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| User: "Major Quaternion Dirt Quantum" |
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| Title: Re: Wired Pendulum |
27 Feb 2007 05:02:37 PM |
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I would add a loop at the V-corner,
just by bending it around more than once;
a little more. of course,
there are all sorts of additional,
minor correlations (exact shape of loop,
as per Huygens' clock e.g.).
thus:
I *do* remember visiting the Bright Side, except that
I just woke "up," there. it was quite obvious, however,
that I really had landed on my head.
it's very hard to simulate lunar gravity
without a suit, except underwater; so,
what is the speed of sound in air, there?
I mistook the actress for a creampuff,
night before last, so I was thinking that
whatsername on the Canadian bills didn't win it;
is this really her first? (anyway, this is why
it's better to have a TV with a blankable picture,
as opposed to submerging the sound,
in that case.)
do you know how many hospitals the ambulance passed-by,
that apparently didn't meet "emergency" standards --
greater or less than 2pi? (I like to compare stuff
with my GPA "goals" .-)
as for Borat,
what was it supposed to have been adapted from,
a semifortnightly sitcom ... a documentary
of ideals that are permissible to hate?
if you haven't logged on to the new 527 cmte.,
algorethemovieforprez.nut, you should be warned,
it's actually a 529 cmte. for your 1.9 children;
the 0.9 is reserved for some sort of trade or
parohcial school, or a combination, like
Harry Potter FAME PS.
I mean, Fame; it's not just Americans
of African desecnt that do it, nor Episcopos.
on the wayside,
someone also stated that
the raito of the "standard" diastole to systole is phi,
or its inverse.
BBC news broadcaster: "It is more that 20,000 miles to the Moon".
thus:
til the Copenhagenschool quackers tried
to eat Schroedinger's undead cat --
is it done, yet !?!
Standard Low Density Lipid - 100
----------------------------------
Standard High Density Lipid - 61.8
--nnerfmann!
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| User: "" |
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| Title: Re: Wired Pendulum |
27 Feb 2007 06:51:23 PM |
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On Feb 27, 7:59 pm, "Freiddy" <fei.yua...@gmail.com> wrote:
So could you please show how you found the answer? Thanks. It doesn't
need to be very detailed, some explanation would be enough.
Freiddy
I should say that my physics classes were a very long time ago, so if
this is mission-critical you should get it checked by a physicist.
(Though in fact I assumed it was homework so I have not written down
all the equations.)
We start with the basic equation
angular acceleration = d^2w/dt^2 = T/I (1)
where w is angular displacement from the vertical, t is time, T is
torque (about the pivot) and I is the moment of inertia (about the
pivot).
I is calculated by summing (integrating) the mass of each
infinitesimal element of the wire, multiplied by the square of its
distance from the pivot.
T is calculated by summing (integrating) the tangential force
generated by the action of gravity on each infinitesimal element of
the wire, multiplied by its distance from the pivot. The tangential
forces are calculated analogously to the simple point-mass-on-massless-
string pendulum. Remember to attend to the signs!
Substitute T and I into (1), do the algebra, make the usual
approximation sin(w) = w for small w, and you get an equation for
simple harmonic motion (analogous to the simple pendulum case), from
which the period can be readily found.
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| User: "Freiddy" |
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| Title: Re: Wired Pendulum |
24 Feb 2007 12:58:09 PM |
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Well? Could you tell me what X is?
Freiddy
http://fei.yuanbw.googlepages.com/
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