## 10.2.2 Defining Equation of Simple Harmonic Motion and Horizontal Spring Mass Model A vs T

- Details
- Parent Category: 02 Newtonian Mechanics
- Category: 09 Oscillations
- Created: Thursday, 20 August 2015 15:00
- Last Updated: Wednesday, 26 December 2018 16:24
- Published: Saturday, 23 April 2016 15:00
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### 10.2.2 Special Case (starting from x=0) Solution to the defining equation:LO (e)*

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)

## 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)

### 10.2.2.1 Model:

- http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM08/SHM08_Simulation.xhtml
- http://iwant2study.org/ospsg/index.php/interactive-resources/physics/02-newtonian-mechanics/09-oscillations/71-shm08

by substitution, suggest if the defining equation a = - ω^{2} x
is true or false.

### 10.2.2.2 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.

### 10.2.2.3 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} |

### Translations

Code | Language | Translator | Run | |
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### Software Requirements

Android | iOS | Windows | MacOS | |

with best with | Chrome | Chrome | Chrome | Chrome |

support full-screen? | Yes. Chrome/Opera No. Firefox/ Samsung Internet | Not yet | Yes | Yes |

cannot work on | some mobile browser that don't understand JavaScript such as..... | cannot work on Internet Explorer 9 and below |

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