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 oscillation problem - help needed

  1. Jun 26, 2004 #1
    "An object is moving along the x-axis in simple harmonic motion. It starts from its equilibrium position which is at the origin at t=0 and is moving to the right. The amplitude of its motion is 2 m and its frequency is 3 hz. (1) Determine the expression for the objects displacement. (2) Where is the object located at t=1.0 s? (3) What is the maximum value of acceleration?

    For 1, using the the general SHM expression, I got x=(2 m) cos (6pi(t) + pi/2)

    But for (2), plugging in 1 sec., i get 2 m. After 1 sec, shouldn't the object be back at the origin?

    For (3), i would really appreciate a hint.

  2. jcsd
  3. Jun 26, 2004 #2


    User Avatar
    Science Advisor

    The amplitude of motion is 2 so the 2 multiplying cosine is correct. The intial position is t=0, x= 0 so the pi/2 gives x(0)= 2*cos(pi/2)= 0 is correct (I would have been inclined to use sin() but probably the formula you were given just uses cos()). The frequency is 3 Hz= 3 cycles per second = 6pi radians per second: Okay, (6pi)t gives you that.

    Now, HOW did you get 2 m. by plugging in t= 1? 6pi(1)= pi/2= 13pi/2 and
    cos(13pi/2)= 0. Did you forget to add that pi/2?

    Since, as you correctly have, x= 2cos(6pi t+ pi/2), v= dx/dt= -12pi sin(6pi t+ pi/2) and a= dv/dt= -72pi2cos(6pi t+ pi/2). The maximum value of that is its amplitude: 72 pi2.
  4. Jun 26, 2004 #3
    Rereading my question, i noticed that i typed the wrong sign in the displacement equation. I meant to say x=(2 m) cos (6pi(t) - pi/2) ["minus" before pi/2]. This now gives 2 m with t = 0. Since the object is first moving to the right (positive), shouldn't the phase angle be -p/2?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook