We differentiate Eq(17-6) twice with respect to the Time 2 @xm cos(at+o) Putting this into Eq(17-5)we obtain k @xm cos(at +o)=--xm cos(@t +o) Therefore, if we choose the constant O such that k (17-7) e Eq(17-6)is in fact a solution of the equation of motion of a simple harmonic oscillatorWe differentiate Eq(17-6) twice with respect to the Time. Putting this into Eq(17-5) we obtain Therefore, if we choose the constant such that (17-7) Eq(17-6) is in fact a solution of the equation of motion of a simple harmonic oscillator. cos( ) 2 2 2 = − x t + dt d x m cos( ) cos( ) 2 −  + = − x t + m k x t m m m k = 2  