text: # Homework Help: Simple Harmonic Oscillator Problem
  
  1. Jan 10, 2013
  
  ### Hibbs
  
  1. The problem statement, all variables and given/known data
  
  The position of a mass that is oscillating on a Slinky (which acts as a simple harmonic oscillator) is given by 18.5 cm cos[ 18.0 s-1t]. What is the speed of the mass when t = 0.360 s?
  2. Relevant equations
  x(t)=Acos(ωt+θ)
  v(t)=-Aωsin(ωt+θ)
  
  3. The attempt at a solution
  
  I used the formula, v(t)=-Aωsin(ωt+θ) because you basically have everything you need such as:
  A=18.5cm
  ω=18.0s^-1
  t=0.360s
  
  What I get is:
  v(0.360)=-(18.5cm)(18.0)sin(18.0*0.360)
  to get -65.1cm/s
  Please tell me where I went wrong!
  
  2. Jan 11, 2013
  
  ### Staff: Mentor
  
  Speed is never negative.
  
  3. Jan 11, 2013
  
  ### rude man
  
  The highlighted formula makes little sense to me. First, the argument of the cos must be dimensionless but here it looks like it's time. 18.0 s must be the phase term but what's with the s? Is 18.0 in radians, deg or ??? The "1" in front of t must be √(k/m), k = spring const. & m = mass, aka ω. The phase is due to the fact that this mass had initial velocity and displacement. Anyway, no way do I see that ω = 18.0.
  
  Weird! I guess you could go
  
  x = 18.5cos(18 - t) cm
  x' = -18.5sin(18 - t) cm/s since I guess ω = 1 rad/s;
  so x'(t=0.36) = -18.5sin(18 - 0.36) = -18.5sin(17.64) cm/s.
  
  BTW v can be negative. Speed can't.
  
  4. Jan 12, 2013
  
  ### ehild
  
  v=-65.1 cm/s is the velocity. The speed is magnitude of velocity.
  
  ehild
  
  5. Jan 12, 2013
  
  ### Staff: Mentor
  
  I believe the formula is just misformatted and is intended to be $\cos(18s^{-1}\times t)$ - so there is no problem with the units.
  
  6. Jan 13, 2013
  
  ### Hibbs
  
  Thanks a lot! I got it!
  
  Last edited: Jan 13, 2013
  7. Jan 13, 2013
  
  ### rude man
  
  OK. What can be done to get the OPs to accurately state the problem, I wonder in my oft leisure moments ...
metadata: {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}