# Special Case (starting from x=0) Solution to the defining equation:LO (e)*

x= x

_{0}sin( ωt )

x= x_{0} sin( ωt ) |

## note:

equation for v can also be obtained by differentiating x with respect to time t.v = x_{0 }ω cos (ωt ) = v_{0} cos (ωt) |

_{0 }ω cos (ωt ) = v

_{0}cos (ωt)

## note:

equation for a can also be obtained by differentiating v with respect to time t.a = - x

_{0 }ω

^{2}sin (ωt ) = - a

_{0}sin (ωt)

a = - x_{0 }ω^{2} sin (ωt ) = - a_{0} sin (ωt) |

## Model:

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM08/SHM08_Simulation.xhtmlby substitution, suggest if the defining equation a = - ω

^{2}x is true or false.

##
Suggest there Special Case (starting from x=x_{0 }) Solution to
the defining equation:LO (e) if given

x= x

_{0}cos( ωt )

v = -x

_{0 }ω sin (ωt ) = -v

_{0}sin (ωt)

a = -x

_{0 }ω

^{2}cos (ωt ) = - a

_{0}cos (ωt)

by substitution, suggest if the defining equation a = - ω

^{2}x is true or false.

## Summary:

Quantity | extreme left | centre equilibrium | extreme right |

x | – x_{0} |
0 | x_{0} |

v | 0 | + x_{0}ω when v >0 or – x _{0}ω when v <0 which are maximum values_{} |
0 |

a | +x_{0}ω^{2} |
0 | –x_{0}ω^{2} |