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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.
There are many situations which call for the replacement of an integral by a sum, or vice versa. In the former case the highest accuracy is sometimes required. This means that in t
a restrained steel bar is heated from 20 degrees to 194 degrees and not permitted to expand. the bar is 10mm diameter, determine the thermal stress in the bar
i
Prove that the Lagrangian coef?cient polynomials for p n (x) satisfy ∑ n k=0 l k (x) = 1. Hint: It is only a 3-line proof. Consider the interpolating polynomial for a constan
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(V^2)dx + x(x+v)dv=0
Find the equilibrium points (real and imaginary parts, to 3 decimal places) if unit positive line charges are placed at a+ic, b+id, and -3-2i. Designate one of these numbers as "m
From this point on it is assumed that any problem amenable to solution with the aid of the Discrete Fourier Transform (or DFT) will in fact be treated computationally with a fast r
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I need a research paper. The concept is to develop a new linear programming was not introduced in the art literature before then apply the LP to spcific industry
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