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Vibrations and Waves: Mass on Incline problem

  1. Apr 20, 2010 #1
    1. The problem statement, all variables and given/known data
    A spring, of negligible mass and which obeys Hooke's Law, supports a mass M on an incline which has negligible friction. The figure below shows the system with mass M in its equilibrium position. The spring is attached to a fixed support at P. The spring in its relaxed state is also illustrated.
    Pic link:

    a) Mass M has a value of 245 g. Calculate k, the spring constant.

    b) The mass oscillates when given a small displacement from its equilibrium position along the incline. Calculate the oscillation frequency.

    2. The attempt at a solution

    I know that I need to find the component of the acceleration due to gravity along the inclined plane. From the graph I can find the sinθ. Then find the force which pulls the spring down. Find the extension of the spring and then k.
    But I dont know how to get started (no ideas how to get numbers on the graph). Please be a guider! Thanks!
  2. jcsd
  3. Apr 20, 2010 #2


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    Length of the unstretched spring is 40 cm.
    Length of the stretched spring is 50*sqrt(2) cm.
  4. Apr 20, 2010 #3
    So, I got the length of the stretched spring is 70.7 cm.
    In order to find k, I need to find F.
    F = -mgsin(theta)
    then I need to find sin(theta) first.
    Could u let me know how to find sin(theta)?
  5. Apr 20, 2010 #4


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    sinθ = opposite side/ hypotenuse.
    From the graph find these values.
  6. Apr 20, 2010 #5
    Hypotenuse = sqrt[60^2+60^2] = sqrt7200 = 84.85
    Sin(theta) = 60/84.85 = 0.707;
    F = -1.700 N. Correct?
  7. Apr 20, 2010 #6
    Got it all. Thanks so much rl.bhat ;)
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