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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 young couple requires RM30000 for an overseas trip which they want to make in six years time. How much they have to invest now at 18% p.a. compound interest compounded monthly, t
A) Prove the following theorem by considering two distinct cases. For any integer n, n 2 + n is even. B) If x = r 2 - s 2 and y = 2rs for any integers r and s, then x 2 +
The following are 8 data points that shows the relationship between the number of fishermen and the amount of fish they can catch a day. (Let the number of fishermen be X and the a
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As an engineering student, the ministry of energy and minerals has tasked you to help them model equation(s) that can estimate the amount of crude oil in a reservoir. The governmen
Values from the iteration x = cos(x) are: x 0 = 0.8, x 1 = 0.696707, x 2 = 0.766959, x 3 = 0.720024, x 4 = 0.751790, x 5 = 0.730468. a) Calculate the sequence {y n } fr
y''=2xy/x^2-y^2
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
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