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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.
outline the three schema database architecture clearly explaining each level and how the user view the information
Let z 0 = a + ic, z 1 = b + id, z 2 = -id, and z = [z 0 + z 1 ]. Let z 0 be the apex of the wedge with one ray passing through z 1 and the other passing through z 2 , and
If x and y are two independent random variables then their joint density function is given by The density function f z of the sum of these two variables is given by the c
Determine the missing entries in the following divided difference table and use the result to estimate f(1/2).
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An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars
application of mathematics in engineering
for what values of (a,b) does the point P (0,a,b) lie on the line through Q (1,-1,4) and R (2,3,5)?
Answer the following set of simultaneous equations using elimination or substitution method. a) x-y +z= 10 b) 3x+y+2z=34 c) -5x+2y-z=-14
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.
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