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looking for a platform to handle harmonic oscillation

Specifically looking for a curve fitting platform for underdamped oscillation

Re: looking for a platform to handle harmonic oscillation

Exactly!!!  You hit a grand slam!  Many thanks!!

Re: looking for a platform to handle harmonic oscillation

Are you trying to just plot an underdamped oscillator?  Or are you trying to fit beta and w0?  The below script will actually fit. 

 

Names Default to here(1);
dt = New Table("Harmonic Oscillator", 
 New Table Variable("beta", .3),
 New Table Variable("w0", .4),
 New Column("t", set values(0::50)), 
 New Column("Cos t", formula(Cos(t))), 
 New Column("Damped Cos t", Formula(
  exp(-:beta*:w0*:t)*cos(:w0*t) + random normal(0, .01) //just adding noise
 )), 
 New Column("Predictor", 
  Formula(
   Parameter({pbeta = .2, pw0 = .5}, 
    exp(-pbeta*pw0*:t)*cos(pw0*t)
   )
  )
 )
);

dt << Nonlinear( Y( :Damped Cos t ), X( :Predictor ), Newton );

 

To give you this.  notice how my actual beta/w0 was .3/.4 but I started my predictor with .2/.5

 

Is this sort of what your'e looking for?

Re: looking for a platform to handle harmonic oscillation

Thanks y'all.  I appreciate the suggetions.  I was able to answer my client's question by fitting an exponential decay curve through my data rather than generate the oscillating underdamped plot.  I would like to figure that part out though.  I need to find some examples to learn from.  Thanks again.

Re: looking for a platform to handle harmonic oscillation

You can give custom equations and parameters in the nonlinear platform.  Also Under specialized models.  

Re: looking for a platform to handle harmonic oscillation

Hacking through that now - thanks.  My data should create a an exponentially decaying sinusoid.  Trying to figure out how to make JMP do it.

Re: looking for a platform to handle harmonic oscillation

In JMP 13, have you looked at

     Anaylze==>Specialized Modeling==>Fit Curve