SHM Chapter 10 a with x

Acceleration

From v = v_o cos ω t = x₀ ω cos ω t
where x_o is the maximum displacement
differentiating we get
 $$a=\frac{dv}{dt}=-{\omega }^2(x_{0}sin\omega t)=-{\omega }^{2}x$$

Variation with time of acceleration   

In terms of x:

Therefore,  a = - xo ω² sin ω t
                   = - ω² (x_o sin ω t)
which is the defining equation for S.H.M. !
               a     = - ω² x

 
Variation with displacement of acceleration 

since 
   
        a = – a₀sin ω t         

where a_o is the maximum acceleration
where by a₀ = ω² (x_o)  

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM10/SHM10_Simulation.xhtml

Model:

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM10/SHM10_Simulation.xhtml