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 = x₀ ω 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 = - x₀ ω² 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