Vipul: /* In terms of the differential equation it solves */

2011-08-12T13:32:45Z

In terms of the differential equation it solves

← Older revision		Revision as of 13:32, 12 August 2011
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	Simple harmonic motion is a form of motion of an object/particle along a line subject to the constraint:		Simple harmonic motion is a form of motion of an object/particle along a line subject to the constraint:

	<math>x''(t) = -\omega^2 x(t)</math>		<math>\! x''(t) = -\omega^2 x(t)</math>

	where <math>x(t)</math> is the position coordinate of the particle at time <math>t</math> and <math>x''(t) = a(t)</math> is the acceleration (signed) of the particle at time <math>t</math>.		where <math>x(t)</math> is the position coordinate of the particle at time <math>t</math> and <math>x''(t) = a(t)</math> is the acceleration (signed) of the particle at time <math>t</math>.

Vipul: Created page with "==Definition== ===In terms of the equation for position=== '''Simple harmonic motion''' is defined as a form of periodic/oscillatory motion along a straight line, with the foll..."

2011-08-12T13:32:06Z

Created page with "==Definition== ===In terms of the equation for position=== '''Simple harmonic motion''' is defined as a form of periodic/oscillatory motion along a straight line, with the foll..."

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==Definition==

===In terms of the equation for position===

'''Simple harmonic motion''' is defined as a form of periodic/oscillatory motion along a straight line, with the following form of equation describing the position coordinate as a function of time:

<math>\! x = x(t) = x_0 + A\sin(\omega t + \varphi)</math>

Here, <math>x_0</math> is the resting position or mean position, <math>A</math> is the ''amplitude'' of oscillation (in that it describes the maximum possible magnitude of displacement from the mean position), <math>\omega</math> is a parameter controlling the frequency (in fact, <math>\omega</math> is <math>2\pi</math> times the frequency of completing one full oscillation), <math>t</math> is the time parameter, and <math>\varphi</matH> is a phase angle.

As a consequence, we have the following descriptions of the velocity and acceleration functions:

<math>\! v(t) = A\omega \cos(\omega t + \varphi)</math>

and

<math>\! a(t) = -A\omega^2 \sin(\omega t + \varphi)</math>

===In terms of the differential equation it solves===

Simple harmonic motion is a form of motion of an object/particle along a line subject to the constraint:

<math>x''(t) = -\omega^2 x(t)</math>

where <math>x(t)</math> is the position coordinate of the particle at time <math>t</math> and <math>x''(t) = a(t)</math> is the acceleration (signed) of the particle at time <math>t</math>.

Simple harmonic motion - Revision history

Vipul: /* In terms of the differential equation it solves */

Vipul: Created page with "==Definition== ===In terms of the equation for position=== '''Simple harmonic motion''' is defined as a form of periodic/oscillatory motion along a straight line, with the foll..."