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with no loss in mechanical energy. In real systems, retarding forces (friction) reduce the mechanical energy and the oscillations are said to be damped. If an external force is applied such that the energy loss is balanced by an energy input, the motion is a forced oscillation. All oscillations arising from elasticity of matter are SHM or a composite of SHM. - tuning fork - stringed instrument - buildings swaying, etc. Fourier: "Any finite periodic motion can be represented as a summation of a number of suitably chosen SHM's" Fourier Series Another important principle is that in any physical situation, sufficiently small displacements from a condition of stable equilibrium result in approximately simple harmonic motion about the potential minimum. Special Case I the mass is extended from equilibrium a distance A and released from rest from this stretched position. x = A v = 0 } t = 0 .: x = A cos ?t v = dx/dt = -?A sin ?t a = d²x/dt² = -?²A cos ?t Figure Displacement, velocity, and acceleration versus time for a particle undergoing simple harmonic motion under the initial conditions that at t = 0, x? = A and v? = 0.

          with no loss in mechanical energy. In real systems, retarding forces (friction) reduce the mechanical energy and the oscillations are said to be damped. If an external force is applied such that the energy loss is balanced by an energy input, the motion is a forced oscillation.

All oscillations arising from elasticity of matter are SHM or a composite of SHM.

- tuning fork
- stringed instrument
- buildings swaying, etc.

Fourier: "Any finite periodic motion can be represented as a summation of a number of suitably chosen SHM's" 
Fourier Series

Another important principle is that in any physical situation, sufficiently small displacements from a condition of stable equilibrium result in approximately simple harmonic motion about the potential minimum.

Special Case I

the mass is extended from equilibrium a distance A and released from rest from this stretched position.

x = A
v = 0 } t = 0

.: x = A cos ?t

v = dx/dt = -?A sin ?t
a = d²x/dt² = -?²A cos ?t

Figure Displacement, velocity, and acceleration versus time for a particle undergoing simple harmonic motion under the initial conditions that at t = 0, x? = A and v? = 0.

with no loss in mechanical energy. In real systems, retarding forces (friction) reduce the mechanical energy and the oscillations are said to be damped. If an external force is applied such that the energy loss is balanced by an energy input, the motion is a forced oscillation.

All oscillations arising from elasticity of matter are SHM or a composite of SHM.

- tuning fork
- stringed instrument
- buildings swaying, etc.

Fourier: "Any finite periodic motion can be represented as a summation of a number of suitably chosen SHM's"
Fourier Series

Another important principle is that in any physical situation, sufficiently small displacements from a condition of stable equilibrium result in approximately simple harmonic motion about the potential minimum.

Special Case I

the mass is extended from equilibrium a distance A and released from rest from this stretched position.

x = A
v = 0 t = 0

.: x = A cos ?t

v = dx/dt = -?A sin ?t
a = d²x/dt² = -?²A cos ?t

Figure Displacement, velocity, and acceleration versus time for a particle undergoing simple harmonic motion under the initial conditions that at t = 0, x? = A and v? = 0.

Added by Leslie D.

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