1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Simple Harmonic Motion (will be the death of me)

  1. Dec 21, 2009 #1
    1. The problem statement, all variables and given/known data
    The motion of an object is simple harmonic with equation of motion x = (27.1 m) sin(16.0 t /s + 0.7). At what time after t = 0 will the displacement reach its first maximum (where velocity equals zero)?

    2. Relevant equations


    3. The attempt at a solution
    "(27.1)(sin((16x)+.7))" into calculator. Where y=displacement and x=time.
    I calculate the first maximum to be at (5.58,27.1). Since the question asks for the time my answer would be 5.58 seconds. But this is wrong, and I'm not sure where I went wrong..

    Any help greatly appreciated, Thanks!
  2. jcsd
  3. Dec 21, 2009 #2


    User Avatar
    Homework Helper

    Hi -Chad-, welcome to PF.
    At the maximum the velocity is zero. So find dx/dt and equate it to zero. From that find arc cos to find t.
  4. Dec 21, 2009 #3


    User Avatar
    Homework Helper

    How did you get t=5.58s ? If I put that value into the equation for x, I don't get 27.1. (Unless my calculator is messing up)
  5. Dec 21, 2009 #4
    Does 3.196 s sound like a better answer?
    I changed my calculator from degrees to radians. (if this fixes my problem, sorry for the stupid mistake)

    If not, rl.bhat, I do not understand what you want me to do. If I take the derivative at the maximum, where velocity is zero, it will also be zero.
  6. Dec 21, 2009 #5


    User Avatar
    Homework Helper

    In the problem dx/dt = (27.1m)(16.0)cos(16*t + 0.7) = 0.
    Now at what angle cosθ = 0?
    Equate that angle to 16*t + 0.7 to find t.
  7. Dec 21, 2009 #6


    User Avatar
    Homework Helper

    How did you get 3.196 s? Derive x = (27.1 m) sin(16.0 t /s + 0.7) and you'll get the equation for velocity. Set the velocity to 0 and you'll be able to solve for t.
  8. Dec 21, 2009 #7
    ?? ok, first rl.bhat, cos90=0 90=16t+.7 89.3=16t 5.58=t (same answer i already got)

    ideasrule, i get the same answer when doing what you want me to do. I'll write out my derivation just for thoroughness.

    product rule______(27.1)(d/dt[sin(16t+.7)])+(d/dt(27.1))(sin(16t+.7))

  9. Dec 21, 2009 #8
    Try using radians, 16t+0.7 = Pi/2
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook