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As with the first order system, there is a general differential equation that governs the response of a second order system. The equation is of the form:
Where:
So how is the second order differential equation for the spring mass damper generated?
Well, if an input is applied to the mass, the equation of motion for the system can be written as:
The general equation for a second order system can be manipulated to give the equation above and vice versa.
Performing the numerical integration for the second order system
The second order equation order is dealt with by rewriting the equation as pair of first order equations. The numerical integration can be performed in a similar way to the first order system where:
Of course as all the hardware information is available or selected by the engineer, the value for (d2y/dz2) can be calculated by manipulating the equation of motion.
Draw concentric circles of radii a and b, each centered at z=id (on the imaginary axis). Suppose φ(x,y) is a harmonic function inside the washer defined by these circles. The circl
First systems were described as systems that had one method of storing energy. Second order systems; wait for it.... have two methods of storing energy. Using a similar mechanica
In closed system 0.3kg of gas at 373K is expanded isothermally and reversibly from 1 mpa pressure to 200 kp. Given that cv= 718 j/kg k and R= 287 j/kgk.
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model an equation to determine the amount of oil in a reservior
what are median,mode,aveage,mode
a) Use divided differences to ?nd the polynomial (in nested form) that interpolates the data b) Add the data point x = 6, y = -20 and hence estimate y for x = 2.
Below are items that affected the 2011 accounting records for Darwin Adaptions Inc. The annual accounting period ended December 31, 2011. No adjusting entries were made during the
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