1. Not finding help here? Sign up for a free 30min 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 involving Spring and Rotating plank

  1. May 6, 2015 #1
    1. The problem statement, all variables and given/known data
    rod-jpg.30343.jpg

    In the overhead view of the figure, a long uniform rod of mass m = 0.24 kg is free to rotate in a horizontal plane about a vertical axis through its center. A spring with force constant 240 N/m is connected horizontally between one end of the rod and a fixed wall. When the rod is in equilibrium, it is parallel to the wall. What is the period of the small oscillations that result when the rod is rotated slightly and released?

    2. Relevant equations

    Torque = rF
    Torque = I*a(angular accel)
    Period = 2pi sqrt(I/k)
    w(angular vel.) = sqrt(k/m)

    3. The attempt at a solution

    So I started by trying to related the torque caused by the spring (Where L is the length of the rod):

    T=r F = (L/2) (-kx)
    x (is the extension of the spring) = (L/2) sinθ
    T= (L/2) (-k)((L/2) sinθ) = (L^2/4) (-k) sinθ
    T= Ia = ((1/12) mL^2) (a)

    (L^2/4) (-kx) sinθ = ((1/12) mL^2) (a)
    a = 3(k/m) sinθ
     
  2. jcsd
  3. May 6, 2015 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Hello.

    Your work looks good. I think you dropped a negative sign in the last equation. Since the oscillations are small, you can make the usual approximation for sinθ.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Pendulum involving Spring and Rotating plank
  1. Springs & Pendulums (Replies: 6)

  2. Pendulum Spring (Replies: 9)

Loading...