Please answer the following questions- let me know if there is background needed as there wasn't any given originally.

Prelab 1: Show that the equations: x(t) = Acos (wt + ) and a(t) = - WAcos (wt + $) solve the harmonic oscillator form of Newton's 2nd Law: at w x =0 (Hint: Do this by substituting the first two equations above into the third and showing 0 = 0.) Prelab 2: The validity of the equation for the period of a pendulum: T = 2n depends on the approximation that: sin 0 ~ 0 Complete the following table (make sure your calculator is in radian mode!): e () (ppl) e sin 0 % Error 2 5 10 15 20 30 where the % error column is the percent error between O in radians and sin 0: 10 - sin e| % error = x 100% We say sin 0 ~ 0 is a good approximation if 0 and sin 0 differ by about 1% at most. Based on this information, for what range of angles is sin 0 ~ 0 a good approximation