### 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