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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.
Solve differential equation of Y" = 0 using the Galerkin method and considering 0 = x= 3 given that: h = 0cm when x = 0m and h = 10cm when x = 3m.
Given the loop transfer function G(s)H(s) = k/s(s+3)(s+4)(s+5) (a) Sketch the root locus plot for G(s)H(s). (b) What is the system gain at s = -1+ 2i? (c) Calculate the
if the sides of a triangle ABC vary in such a way that it''s circum-radius remains constant. prove that, da/cos A+db/cos B+dc/cos C =0
#quExample - Electronics application of 3×3 System of Equations Find the electric currents shown by solving the matrix equation (obtained using Kirchhoff''s Law) arising from this
A manager has determined the cost C, in dollars, for manufacturing is C(q) =85log 10 (10+q/2) for manufacturing, where q is the number of units produced in a given day. (a
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 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
Verify how long $400 must be left to store at 12 % p.a. compounded monthly for it to amount to triple the soted value of another $400 deposited at the similar time at 8.8% p.a. com
y"+3y''+2y=0
An experiment conducted over time T necessarily produces a windowed view of the phenomenon generating the data. It is a useful strategy to regard the windowed data as one period of
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