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Simple Harmonic Motion

  1. Dec 3, 2003 #1
    The bow of a 5.0E6 kg destroyer undergoes a simple vertical harmonic motion with a period of 8.0 s and amplitude of 2.0 m. The motion of the boat is recorded by a sailor. At t = 0 s, the boat is at 40 cm above the equilibrium point with an initial velocity of -25 cm/s.

    a) Find the phase constant, the angular frequency, and write the equations of motion, velocity, and acceleration.

    -----
    Sadly enough, I'm having trouble finding the phase constant. I'm not sure exactly what I'm doing wrong...but due to circumstances I don't have the correct answer to look at, only one incorrect one. There are more parts to this problem but I haven't tried them yet, since I'm stuck here... So I may edit this post with another question when I can figure this one out.

    I'm using x = A cos (wt + phi) , .4 = 2 cos [(-.25)(0) + phi] which gives me 1.37, the incorrect answer.

    ***/Edit***
    d) A 90-kg sailor is standing on a scale in a bankroom near the bow. What are the maximum and minimum readings on the scale in Newtons?
    - For this one would I just use a(max) = (omega^2)*A and add that to 9.81 to get the acceleration. Then multiply that by his mass? For the minimum I would just subract a(max) from gravity and do the same?

    e) The ship main computer is mounted on a suspension system to protect it against vibrations and shocks. Protected by this system, a 20 Hz oscillation loses half its energy in .5 s. What are the fractional energy loss per cycle and the Q factor of the suspension system? - Absolutely no clue on this one.
    ***/Edit Off***


    Thank you for your time and any help is greatly appreciated!

    -Edge
     
    Last edited: Dec 3, 2003
  2. jcsd
  3. Dec 3, 2003 #2

    HallsofIvy

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    .4 = 2 cos [(-.25)(0) + phi] so cos[phi]= 0.2 and therefore
    phi= arccos(0.2)= 1.37 radians OR arccos(0.2)= 78.48 degrees. Is it possible that your book has the phase angle in degrees rather than radians?
     
  4. Dec 3, 2003 #3
    Well the GTA for my class is who said that answer was wrong so maybe he just misread it? I'm not really sure of any other way to find the phase constant. Oh well, I really do appreciate the help! I'm just about to update my post with another part of the problem, if you'd like to try to help on that one too.

    -Edge
     
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