6 - Assume both ends of the column are hinged, and solve....

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Example Determine the steady-state current in an LRC series circuit when the impressed voltage is E ( t ) = 3sin4 t.
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Aside: Undetermined Coefficients (aka we’re smart so we can make a good guess!) Idea: For non homogeneous, consider f ( x ) f(x) Solution has form:
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Beams
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Carrying a load: If deflection is small, then
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Embedded Cantilever Hinged
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Example Determine the deflection y ( x ) of a loaded beam of length L that is embedded at the left end and simply-supported at the right end and subject to a constant load of 2 EI .
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Example Consider a slender vertical column of length L subject to a constant compressive load P applied to the top. This is modelled by the differential equation:
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Unformatted text preview: Assume both ends of the column are hinged, and solve. Power Series Solutions Consider the 2 nd-order homogeneous differential equation: Put it into standard form: Definition: f ( x ) is analytic at x means that is an ordinary point of Definition: A point x If Definition: A point x is a singular point of the equation if Lecture 8 Page 1 Theorem If x is an ordinary point of then we can always find two linearly independent solutions in the form of a power series at x 0. (Theses solutions will be convergent on some interval around x 0. ) Example Solve y + y = 0. Lecture 8 Page 2 Lecture 8 Page 3...
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This note was uploaded on 11/10/2010 for the course DEFFERENTI 2080 taught by Professor Kidnan during the Spring '10 term at UOIT.

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6 - Assume both ends of the column are hinged, and solve....

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