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Discussion: All in Calculus
Topic: Simple Harmonic Motion (SHM)
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Subject:   Simple Harmonic Motion (SHM)
Author: Sione
Date: Feb 4 2004
No, it is different. The one that you described "function flyer" is a function
plotter, although you can plot an SHM as well as any "sinusoidal" function such
as "sin(x)" , "cos(x)" , blah, blah , blah.

>you simply type in something like "3*sin(1.4*(x-2))+1" >as the function

The function you described "3*sin(1.4*(x-2))+1" cannot be physically (Physics)
possible to be called as SHM since the  max displacement is "+4" (ie, 3+1) to
the positive direction, and the min displacement is "-2" (ie, -3+1) to the
opposite (negative direction). Have you seen any pendulum (real physical SHM)
that swings past the vertical line (equilibrium position) to the right (positive
direction) by say 15 degrees and swing to the left (negative or opposite
direction) past the vertical again only to 10 degrees? SHM Physics does not
happen this way. It the pendulum is displaced by say 15 degrees to the right and
released , it will swing past the vertical to the left and reached a max of 15
degrees. That is they are both the same in either direction.

The applet is got nothing to do with demonstration of the principles of SHM
although it is a good plotter. The applet I wrote, involves plotting
displacement 'x(t)' , the velocity 'v(t)' which is [ v(t) = dx(t)/dt] , the
first derivative of the displacement, acceleration 'a(t)' which is [ a(t) =
dv(t)/dt = d/dt(dx(t)/dt)], the first derivative of velocity and also equals to
the second derivative of displacement. Same for the force F(t) which is [F(t) =
M*a(t) , ie mass times acceleration]. The user can read at what position 'x(t)'
is the the velocity is 'v(t)' is max or min or what velocity 'v(t)' is the force
exerted on the pendulum or "spring-mass" SHM system is maximum or minimum. You
can tell those Physics observables (variables) from the applet I wrote but you
cannot do that with the "function flyer".


On Feb 04, 2004, Craig Russell wrote:

The tool "function flyer" at does much the
same thing--you simply type in something like 3*sin(1.4*(x-2))+1 as the
function, then it automatically places sliders on each of the four parameters.
This is a very versatile tool (and very smart, too-- if you put integer
parameters, the sliders stick with integers), useful for most any elementary
function family.

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