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Another Problem (spring)

  1. Nov 14, 2004 #1
    A spring with spring constant 230 N/m vibrates with an amplitude of 12.0 cm when 0.530 kg hangs from it.

    (a) What is the equation describing this motion as a function of time? Assume the mass passes through the equilibrium point, toward positive x (upward), at t = 0.120 s.

    The equation is:

    (b) At what times will the spring have its maximum and minimum lengths? (Consider only the first instances after t = 0.)

    (c) What is the displacement and direction at t = 0?

    (d) What is the force and its direction exerted by the spring at t = 0?

    (e) What is the maximum speed?

    When is it first reached after t = 0?
  2. jcsd
  3. Nov 14, 2004 #2
    So? What have you tried so far?
  4. Nov 14, 2004 #3
    I was able to find both A and w, but I can't find the phase angle...and i think everything else that follows requires it.
  5. Nov 14, 2004 #4
    You have x(t)=Acos(wt+phi). Also, you know x(0.120)=0. Do you think this might be sufficient to determine phi?
  6. Nov 14, 2004 #5
    (In addition, of course, you have to note that x is increasing at 0.120 s)
  7. Nov 14, 2004 #6
    I need help solving for c. I know that minimum length equation is -12=12*cos(wt+phi) and maximum is 12=12*cos(wt+phi), and I only w and phi, how do I solve for t using algebraic operations?
    Last edited: Nov 14, 2004
  8. Nov 15, 2004 #7
    Please, anyone?
  9. Nov 15, 2004 #8


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    Staff Emeritus
    Science Advisor

    What IS c? Your original problem made no mention of "A", "w", or "C". Are you referring to phi, the phase angle still? But then you end with "how do I solve for t using algebraic operations?" Did you mean "t" instead of "c"? Which t do you want? t is a variable.
  10. Nov 15, 2004 #9
    OK, I was able to figure out parts a and c. But for b) and e) when I solved for t, it's negative. So how to I find instances after t=0?

    Also, Isn't d) just F=-kx? But the force given by the book is so small compared to my answer.
  11. Nov 15, 2004 #10

    Doc Al

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    Staff: Mentor

    The motion is periodic: it repeats exactly every period. (What's the period?)

    Yes, the force obeys Hooke's law. That probably means you found the wrong displacement at t = 0.
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