2 Problem 2 Consider a simple harmonic oscillator whose Action is given by S = dt m -(()) dt [90 points] (1) here x is a function of time i.e x(t). 1. Use equation 1 and by doing integration by parts show that (here the upper limit is t₁₁ and lower limit is t₂ = x2) S dt 1 1 3-(-) : = √ at (- 2 dt2 Hint: The boundary terms can be taken to be zero i.e: [] (2)