Nonlinear equation

result1 = 
      NDSolve[{y''[t] == -Sin[y[t]], 
          y[0] == Pi/2, y'[0] == 0}, 
        y, {t, 0, 10}]

plot1 = Plot[y[x] /. result1, {x, 0, 10}];

Linear equation

result2 = 
      NDSolve[{y''[t] == -y[t], 
          y[0] == Pi/2, y'[0] == 0}, 
        y, {t, 0, 10}]

plot2 = Plot[y[x] /. result2, {x, 0, 10}];

Show[plot1, plot2]