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Adding a damping force proportional to x^. to the equation of simple harmonic motion, the first derivative of x with respect to time, the equation of motion for damped simple ...

Critical damping is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0, (1) in which D=beta^2-4omega_0^2=0, (2) where beta is the damping constant. ...

Simple harmonic motion refers to the periodic sinusoidal oscillation of an object or quantity. Simple harmonic motion is executed by any quantity obeying the differential ...

The word "harmonic" has several distinct meanings in mathematics, none of which is obviously related to the others. Simple harmonic motion or "harmonic oscillation" refers to ...

Overdamped simple harmonic motion is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0, (1) in which beta^2-4omega_0^2>0. (2) Therefore ...

Underdamped simple harmonic motion is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0 (1) in which beta^2-4omega_0^2<0. (2) Since we have ...

Given a simple harmonic oscillator with a quadratic perturbation, write the perturbation term in the form alphaepsilonx^2, x^..+omega_0^2x-alphaepsilonx^2=0, (1) find the ...

A Euclidean motion of R^n is an affine transformation whose linear part is an orthogonal transformation.

The type of motion executed by a dynamical system containing two incommensurate frequencies.

A function of the coordinates which is constant along a trajectory in phase space. The number of degrees of freedom of a dynamical system such as the Duffing differential ...