SH0W Y0UR C0MPLETE S0LUTION (and wr1te it on a paper)

Consider the equation for simple harmonic motion (SHM) a(t) = wzs(t) Where a(t) is the linear acceleration, s(t) is the displacement from the equilibrium point, a) is the angular frequency, and t is the time. 1. Verify that Accos(ot + 5) and Assinoot + 5) satises the SHM equation for an arbitrary constant phase 6 and arbitrary constant amplitude A: or A5. 2. Consider an exponential ansanlz expt) where A is to be determined: a) What are the allowed values of 1 so that the ansatz will satisfy the SHM equation? b) Write down the general solution of the SHM equation using the exponential ansatz with the allowed A c) is it possible to rewrite the exponential solution in terms of either the sine or cosing functions (choose one)? Relate the constants in the exponental form with the constants in the trigonometric form in item 1