energy = f(amplitude, freq)
energy = f(amplitude, freq)
(OP)
What is the relationship to express power required to force an object to vibrate a varying amplitude and frequency for a known mass, spring constant, and damping value?
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RE: energy = f(amplitude, freq)
RE: energy = f(amplitude, freq)
<p(t)> = Frms * Vrms * cos(theta) where
<p(t)> = average value of power
Frms = Fpeak/sqrt2
Vrms = Vpeak/sqrt2
theta = time angle between F and V
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RE: energy = f(amplitude, freq)
V = velocity
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RE: energy = f(amplitude, freq)
(where w is not necessarily its natural frequency) then its velocity is given by v = aw*cos(wt).
From these formulae it follows that when the object is at its equilibrium position (t = 0, ?/w, 2?/w, ...) the system's total energy is m*(aw)2/2 (since it is entirely kinetic). Similarly when the object is at one of its two extreme positions (t = ?/(2w), 3?/(2w), 5?/(2w), ...) the system's total energy is k*a2/2 (since it is entirely potential).
When the characteristics of the vibration (a and/or w) are changing with time, then the changes in the system's total energy are the result of energy losses due to damping and/or work done on the system by some external force (or work done by the system on an external force). To take things further you need to know the damping model and the external force as a function of time. You can then set up the appropriate differential equation: this might have an analytical solution, or might require a numerical solution. Standard textbooks on dynamics will present the derivation and solution for the case where the damping is "viscous" and the external force varies sinusoidally.
[Note that if we have no damping and no external force, the system's total energy will be constant. We can then equate the two energy formulae above and solve for the system's natural frequency, hopefully getting w = ?(k/m).]
RE: energy = f(amplitude, freq)
RE: energy = f(amplitude, freq)
RE: energy = f(amplitude, freq)
If the system is
Mass
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K C
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Ground
where sinusoidal force is applied to the mass in steady state:
<p(t)>=v * F = v^2 * c = w^2*x^2*c
where w = 2*Pi*f
f = frequency
F = force (rms)
v = velocity (rms)
x = displacement (rms)
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RE: energy = f(amplitude, freq)
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Eng-tips forums: The best place on the web for engineering discussions.
RE: energy = f(amplitude, freq)
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RE: energy = f(amplitude, freq)
average power input is
<p(t)>=(2*pi*f*x)^2 * c
where f is frequency and x is rms displacment.
I assumed sinusoidal steady state, linear time invariant system in configuration shown above.
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RE: energy = f(amplitude, freq)
Thanks for you help.