A 0.47 kg air cart is attached to a spring and allowed to oscillate. You are given the displacement of the air cart from equilibrium to be x = (21.0 cm) cos[(3.74 s^{-1})t + π].

(a) Find the maximum kinetic energy of the cart. J (b) Find the maximum force exerted on it by the spring. N

The displacement is:
x(t) = A cos(w t+pi) = A[cos(wt)cospi - sin(wt)sinpi]= -A coswt
A = 21.0 cm = 0.21 m ; w(omega) = 3.74 s^-1.
The speed is: v = dx/dt = Aw sin(wt)
The maximum speed is : V = A w = 0.21*3.74 = 0.7854 m/s
(a) The maximum kinetic energy is :
Kmax = (1/2) m V^2 = 0.5*0.47*0.7854^2 = 0.145 J
(b) The maximum force is :
Fmax = m a-max = m A w^2 = 0.47*0.21*3.74^2 = 1.38 N