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Problem wit h a pendulum

  1. Sep 29, 2013 #1
    1. The problem statement, all variables and given/known data

    A pendulum clock measures the time exactly if its period is [itex] T_0 [/itex]. What time does the pendulum record in a time [itex] D [/itex] , if its period becomes [itex] T [/itex] ?

    2. Relevant equations

    I know that the number of oscilations of the pendulum in the time D is : N=D/T

    3. The attempt at a solution

    Well I don't know how to use the informations that the probelm gives me.






    P.S. : SORRY FOR THE SPELLING IN THE TITLE
     
  2. jcsd
  3. Sep 29, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    Each period of the pendulum, the display of the clock goes forwards by T0.
    After N periods, what does the clock show?
     
  4. Sep 29, 2013 #3
    Ohhhhh I get it now. I looked more closely in the mechanism of the pendulum. From what I understood, each time an oscilation is completed the pendulum records a certain time. Let this time be [itex] t [/itex]. This [itex] t [/itex] is constant, and its typical for every pendulum, right ?

    In our problem the period , i.e. the time needed for an oscilation to be completed , is modified. But, because our [itex] t [/itex] is a constat, the pendulum will record the same time for each oscilation, even if the number of oscilations increases or decreases.

    In our problem:

    In a time D, the pendulum swings : [itex] N=\frac{D}{T} [/itex] times => the pendulum measures the time [itex] Nt [/itex] .

    Who is [itex] t [/itex] ? Well we know, from the hypothesis that [itex] \frac{D}{T_0}t=D [/itex], that is , if the period is [itex] T_0 [/itex] then the time measured by the pendulum is D. Solving for t, we obtain: [itex] t = T_0 [/itex] .

    So, [itex] Nt = NT_0=\frac{D}{T}T_0 [/itex]. This is the time the pendulum measures.

    Please, help me, and tell me if my judgement is correct. I belive that what confused me before was that I wasn't fully aware that the mechanism of a pendulum allows it to record the same amount of time, and that this time ( [itex] t [/itex] ) doesn't depend on the number of oscilations.
     
  5. Sep 29, 2013 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Right.

    Correct.
     
  6. Sep 29, 2013 #5
    Thank you very much!!!!
     
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