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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.
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simple problems on partial derivatives
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
The P.D. at the feeder end of a two wire d.c. distributor is 600 volts. Two loads are connected to the distributor at distances of 600 feet and 1000 feet from the feeder end and t
y"+3y''+2y=0
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Below are the conditions specified by the institution: a) If the temperature sensor shows 30 degree Celsius or higher, the air-conditioner will be turned ON regardless of the othe
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
A scientist calculates the temperature of melting platinum using a new type of thermometer. The temperature of the metal is called to be exactly 1768.3 centigrade. The measurements
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