Tuesday, January 13, 2015

SHM Chapter 08 x,v,a vs t

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


x= x0  sin( ωt )

x= x0  sin( ωt )


    

note:

equation for v can also be obtained by differentiating x with respect to time t.
v = xω cos (ωt ) = v0 cos (ωt) 
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)
a = - xω2 sin (ωt ) = - a0 sin (ωt) 


Model:

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM08/SHM08_Simulation.xhtml
by substitution, suggest if the defining equation a =  - ω2 x is true or false.

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.



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