Consider the second order differential equation corresponding to a damped harmonic oscillator.d2xdt2+ α1dxdt + α2x = Discretize this equation, using a time step of ∆, and do the following:(a) Express it as an AR(2) process xt = φ1xt−∆ + φ2xt−2∆ + wt being sure to clearly link the φ’s to the α’s. Let ∆ = 1 and provide R code that simulates a realization with σ2w = 1,and φ1 = 1.5 and φ2 = −0.75.(b) Now, express the AR(2) process as an multivariate AR(1)model. Provide R code and simulate the identical realizations to part (a). (Note: you will need to set the random number seed to be the same).
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