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SHM08

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

x= x0  sin( ωt )
     

Note:

Equation for v can also be obtained by differentiating x with respect to time t.

v = x0 ω cos (ωt ) = v0 cos (ωt)
   

Note:

Equation for a can also be obtained by differentiating v with respect to time t.


a = - x0 ω2 sin (ωt ) = - a0 sin (ωt)

10.2.2.1 Model:

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

by substitution, suggest if the defining equation a =  - ω2 x is true or false.

10.2.2.2 Suggest there Special Case (starting from x=x0 ) Solution to the defining equation:LO (e) if given

x= x0  cos( ωt )
v = -x0 ω sin (ωt ) = -v0 sin (ωt)
a = -x0 ω2 cos (ωt ) = - a0 cos (ωt)

by substitution, suggest if the defining equation a =  - ω2 x is true or false.

10.2.2.3 Summary:

Quantity extreme left centre equilibrium extreme right
x – x0 0 x0
v 0 + x0ω when v >0 or
– x0ω when v <0 which are maximum values
0
a +x0ω2 0 –x0ω2
 

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Parent Category: 02 Newtonian Mechanics
Category: 09 Oscillations
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