9. We return to the circle of radius 5 in 2-dimensional space centered at the origin, with our original parameterization of this circle as r(t)= (5 cos (t), 5 sin(t)), where t runs from 0 to 2. (a) If this parametrization represents the motion of a particle around a circle, how far has the particle traveled from time 0 to time t? We'll call this distance s. Write s as a function of t. (b) Solve for t in terms of s and plug this into your parameterization to get a new parameterization r(s). (This is called a parameterization by arc length or an arc length parametrization.) What do you notice about it?

b. A particle moves in simple harmonic motion according to the equation, S = 09A cos(wt) + 09B cos(wt). Where s is the displacement, w is the angular d2 +ws=0. 'dt2 frequency and A, B are constant. Show that,

b. A particle moves in simple harmonic motion according to the equation, s = A cos(wt)+ B sin(wt). Where S is the displacement, w is the angular d²s frequency and A, B are constant. Show that, dt2 + w?s = 0.