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Simple Harmonic Motion Lab Question

  1. Apr 8, 2009 #1
    In physics class, we had to do a lab where a mass was attached vertically to a spring system. The spring went through simple harmonic motion. We stretched the mass and let go of it. We then used a software to determine the kinetic energy, the elastic potential energy, and the total energy. We had to predict what the total energy graph would look like. I thought that it should be constant, as according to the law of conservation of energy. However, from the graph that I got from the observations, the total energy increases and decreases. What would be the reason for this? Would human errors have anything to do with this, such as not being able to get the spring to move completely vertically. Would my observations show that the mass and spring system does not follow the conservation of mechanical energy?
  2. jcsd
  3. Apr 8, 2009 #2
    The sum of kinetic plus potential energy (H = T + V) should be a constant of the motion, unless it is damped, but H should not increase. Have you measured the spring constant k and the mass m accurately? Have you measured the oscillation frequency, and does it equal
    w= sqrt(k/m) radians/sec?
    If not, remeasure k, m, and w again. Does the spring constant k depend on displacement (i.e., nonlinear displacement)? Does w depend on amplitude of motion (maximum extension of spring)? How rigid is the anchor for the spring? How accurately are you measuring the maximum spring extension and the maximum velocity during the oscillations?
  4. Apr 8, 2009 #3
    When the mass was stretched an let go of, it was moving somewhat sideways. Would this have somewhat to do with it? Wouldn't some of the mechanical energy be converted into thermal energy as a result.
  5. Apr 8, 2009 #4


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    Staff: Mentor

    Damping (what slows it down) converts mechanical energy into thermal.

    A graph of the total energy should be a hyperbola with 0 as its asymptote.
  6. Apr 8, 2009 #5


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    Staff: Mentor

    Many springs twist slightly as they stretch and contract, and objects hanging from them acquire rotational motion (with rotational kinetic energy) as a result. Did you notice any rotational oscillatory motion of your mass?
  7. Apr 8, 2009 #6
    I don't think there was any rotational motion but it was moving somewhat sideways. Also, mechanical energy is only composed of kinetic energy and elastic potential energy. Since some of the total energy is lost to thermal energy due to air resistance, the mechanical energy is bound to change. Am I correct in assuming this?
  8. Apr 8, 2009 #7
    how does one "observe" total energy while in osciallation? you can only really observe potential or kinetic and then add them together to get total. i would think the total energy put into the system would be equal to the work done to get motion going (eg pulling down on the mass attached to spring, etc). then you'll observe the potential and kintic energy oscillate with a phase shift of 180 degrees and equal at 90 degrees. the damping factor will govern how that work done dissipates.

    if the movement is in more than one axis then you'll need to observe the energy as vector components and summarize, but that total must equal the work done to pull down the mass attached to spring, etc. probably very hard to do if its bouncing all over the place, etc.
  9. Apr 9, 2009 #8
    If you think about the turning point in your oscillation (i.e. when the mass is at its lowest point) your total energy is just (1/2)*k*x^2. If you're saying that your total energy is decreasing AND INCREASING you're saying that as time goes on the lowest your spring goes INCREASES (and decreases). Which I'm going to go out on a limb and say didn't happen. Now it is true that your "total energy" is going to decrease because a real world spring system is a damped oscillation so it loses some kinetic/potential energy to heat with each oscillation. However, it will never increase (with in the error of your measurement)
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