In[]:=
g=9.81;l0=0.2;m=0.90;k=10;​​sol=NDSolve[{x''[t]==(l0+x[t])*(theta'[t])^2-(k*x[t])/(m)+g*Cos[theta[t]],theta''[t]==(-2*theta'[t]*x'[t])/(l0+x[t])-(g*Sin[theta[t]])/(l0+x[t]),x[0]==0.05,x'[0]==0,theta[0]==0.35,theta'[0]==0},{x[t],theta[t]},{t,0,100}];​​ParametricPlot[{t,x[t]}/.sol,{t,0,50}]ParametricPlot[{t,theta[t]}/.sol,{t,0,50}]
Out[]=
10
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50
-0.3
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-0.1
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0.5
1.0
1.5