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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.
y''=2xy/x^2-y^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
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the solution of diffusion equation by using separation of variables
This is a pen and paper exercise, you are expected to provide a detailed derivation. Follow the procedure outlined in the lectures for construction of a simple averaging by thr
y"+3y''+2y=0
An electronic module is mounted on a machine and is modelled as a single degree of freedom spring, mass, and damper. During normal operation, the module of mass m kg is subject to
The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to
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A company's full profit per unit production is given by the function y = -5x 2 +17x-12 where x is the number of items produced (in hundreds) and the y is the profit per unit (in
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