1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Pendulum Tilted at an Angle

  1. Nov 14, 2015 #1
    1. The problem statement, all variables and given/known data
    What would the period be if the pendulum had been inclined to 90 degrees? What value of g does this correspond to?
    theta=90degrees. Just as a side note, theta=0degrees when the arm is facing vertically downwards towards the ground.
    g=9.8m/s^2
    Effective length=0.275m. The value of length was found from the lab I carried out.
    Mass attached to end of arm=0.176kg
    2. Relevant equations
    T=2pi x root(L/gcostheta) T is period.
    ag=gcostheta. ag is acceleration due to gravity.
    3. The attempt at a solution
    T=2pi x root(0.275m/(9.8 x cos90))=undefined. Since ag=gcostheta=(9.8 x cos90)=undefined, there would be no acceleration acting on the pendulum, thus no force pushing the pendulum. As a result, the pendulum will not oscillate, and there would be no period. I'm not sure if this is correct, would a pendulum still oscillate when the arm is tilted at 90degrees, and how can period be undefined?
     
  2. jcsd
  3. Nov 15, 2015 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    What if you think of it in terms of the angle tending to 90 degrees? What does the period tend to?
     
  4. Nov 15, 2015 #3
    Remember that the equation T=2pi x root(L/g) T is period was derived
    for small angles where sin theta approximately equals theta (usually less than 10 deg).
    where did the equation T=2pi x root(L/gcostheta) come from?.
     
  5. Nov 15, 2015 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    racwen is interpreting the problem as a pendulum with a tilted plane of oscillation. Given the question about the value of g, that does seem to be the right view.
     
  6. Nov 15, 2015 #5
    OK, so theta in this sense is a constant in the derivation of the equation of a simple equation.
     
  7. Nov 15, 2015 #6
    The period depends on the length, and acceleration (including the angle). I'm not sure if that's what you mean?
     
  8. Nov 15, 2015 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    No, I mean suppose it is tilted at some angle theta. You found the period for that. Now, instead of substituting theta equals 90 degrees, consider what happens to the period as theta tends towards 90 degrees. What value does the period tend to?
     
  9. Nov 15, 2015 #8
    As period approaches 90 degrees, the period increases. It goes past approximately 25.27s when I used theta=89.9degrees.
     
  10. Nov 15, 2015 #9

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes, but what is the value in the limit as theta goes to 90?
     
  11. Nov 15, 2015 #10
    As theta approaches 90, the limit approaches infinity.
     
  12. Nov 15, 2015 #11

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Right.
     
  13. Nov 15, 2015 #12
    So if the period does not exist at 90degrees, does that mean that the pendulum takes an infinite or unknown amount of time to complete one cycle?
     
  14. Nov 15, 2015 #13

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The reason I took you through that approach using limits was to demonstrate that it is known.
     
  15. Nov 15, 2015 #14
    Ohh ok, thank you for your help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted