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:
- 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 = - 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 |