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Coupled physical pendulums ( )

  1. Oct 24, 2012 #1
    Coupled physical pendulums (URGENT)

    Imagine that you have coupled physical pendulums like this (see image below).

    Imagem 1.jpg

    mass is in the inferior part of the pendulum.*

    Now we let the right pendulum swing without initial speed = 0 with a certain amplitude.


    As we know, the amplitude of the right pendulum will decrease , increasing the amplitude of left pendulum.

    I have the Period for the max amplitude of the right pendulum. When the amplitude of the right pendulum is zero, i have to mark the max amplitude of the left pendulum.

    You can see in the following image:
    Imagem 2.jpg

    L it's approximated 1 meter.

    d its caused by the coupled pendulums. it's the distance between the equilibrium point without being coupled to the equilibrium point being coupled.

    Now how can i calculate the frequency (v max) of the left pendulum??

    I just know the period of the right pendulum. I know the max amplitude in left pendulum. How can i calculate the frequency of the left pendulum?

    ( frequency is induced by right pendulum)?


    I really need help, its urgent.
     
    Last edited: Oct 25, 2012
  2. jcsd
  3. Oct 25, 2012 #2
    Re: Coupled physical pendulums (URGENT)

    anyone??is something my problem that is not explicit?
     
  4. Oct 25, 2012 #3
    Re: Coupled physical pendulums (URGENT)

    TBH, I can't make head or tail of it.
     
  5. Oct 25, 2012 #4
  6. Oct 25, 2012 #5
    Re: Coupled physical pendulums (URGENT)

    The diagram looks like no coupled pendulum arrangement I've ever seen.

    You seem to have a rigid bar on the right - which could be a pendulum except that it has no mass associated.
    On the left is another bar, this time with a mass so I assume that IS a pendulum. And between them you have a mass suspended on a cord.

    The nearest thing to this in standard physics texts is two pendula coupled by a spring. The analysis of the motion is not simple.
    Try http://http://www.theorphys.science.ru.nl/people/fasolino/sub_java/pendula/doublependul-en.shtml
     
  7. Oct 25, 2012 #6
    Re: Coupled physical pendulums (URGENT)



    that link is not working. :/
     
  8. Oct 25, 2012 #7
    Re: Coupled physical pendulums (URGENT)

    i found this equations to coupled pendulums.




    I= inertial

    α and β are angles.

    M1 = mass of right pendulum
    L1 = length of right pendulum = L2
    m2 = mass of left pendl..

    For the right pendulum:
    I1.d^2α/dt^2 = -1/2.M1.g.L1.sinα - k[sinα - sinβ]

    For the left pendulum:

    I2.d^2β/dt^2 = -1/2.m2.g.L2.sinβ k[sinα - sinβ]



    in the limit of small angles

    α,β << 1
    so:

    I1.d^2α/dt^2 = -1/2.M1.g.L1.α - k[α-β]

    I2.d^2β/dt^2 = -1/2.m2.g.L2.β + k[α-β]


    if we consider a weak coupled pendulum system, then:

    k<<1

    and because left pendulum have a mass and a inertia much greater then the right pendulum:

    M1>>m2 and I1>>I2

    Equation to right pendulum can be simplified to:

    I1.d^2α/dt^2 ≈ -1/2.M1.g.L1.α


    to left pendulum we have:

    I2.d^2β/dt^2 = -[1/2.m2.g.L2.β+ kβ ] + kα

    i.e

    I2.d^2β/dt^2 + (ωo)^2.β = kα(t)




    then

    (ωo)^2 = 1/2 * (m2gL2) + k

    so the frequency induced by the right pendulum to the left pendulum is:

    f = 2.pi/ωo ......

    is that right?
     
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