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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.
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.
A new gantry crane for a metal fabrication shop is to be designed. The designer has proposed the following two different configurations: A. Using only truss elements B. Using the
y"+3y''+2y=0
i want assignment or notes on curve tracing in polar form and cartesian form
Define a mapping from the x,y plane to the u,v plane by u = 2x + y, v = -x +2y . If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 de
How to solve the problems
y''=2xy/x^2-y^2
You are working as an engineer on a project that involved being able to accurately measure the fluid level change in a large outdoor holding tank. The fluid level rises and falls a
In an article in Marketing Science , Silk and Berndt investigate the output of advertising agencies. They describe ad agency output by finding the shares of dollar billing volume
integral dx/root of sinx using beta and gamma functions
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