Characteristic equation

Thread starter Ry122
Start date Apr 2, 2009
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Characteristic Characteristic equation

In summary, a characteristic equation is an algebraic equation used to relate coefficients and roots of a polynomial function. It is solved by factoring and setting each factor equal to zero, and is important in fields such as mathematics and physics for solving complex problems. These equations can have complex roots, which are commonly solved using the quadratic formula. In physics, the characteristic equation is used to find natural frequencies of systems and solve differential equations.

Apr 2, 2009

Ry122

For the ODE x''+2x'+6x=sin2t
what is the characteristic equation?
Is it m^2+2m+6=0
or m^2+2m+6=cos2t

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Apr 2, 2009

dirk_mec1

The first one.

1. What is a characteristic equation?

A characteristic equation is an algebraic equation that relates the coefficients and roots of a polynomial function. It is commonly used in mathematics and physics to solve for unknown variables.

2. How is a characteristic equation solved?

The characteristic equation is solved by factoring the polynomial function and setting each factor equal to zero. The resulting values are the roots of the function, which can then be used to solve for the unknown variables.

3. What is the importance of the characteristic equation in science?

The characteristic equation is important in science because it allows us to find the solutions to complex problems involving polynomial functions. It is used in a variety of fields, including physics, engineering, and economics.

4. Can a characteristic equation have complex roots?

Yes, a characteristic equation can have complex roots. This is common in higher order polynomials and is often solved using the quadratic formula or other methods.

5. How is a characteristic equation used in physics?

In physics, the characteristic equation is used to solve for the natural frequencies of a system, such as a vibrating object or a circuit. It is also used in differential equations to find the solutions to physical systems.