A 0.64-kg air cart is attached to a horizontal spring and allowed to oscillate. The horizontal position of the air cart is modeled with the function x = (0.5 m)sin(8.4 πt)

(A) Where is the cart at t = 0 sec?

(B) What is the amplitude of the cart's motion?

(C) Calculate the period of the oscillation.

(D) Calculate the frequency of the oscillation.

(E) What is the spring constant of the spring?

(F) What is the magnitude of the maximum force exerted on the cart by the spring?

(G) What is the maximum speed reached by the air cart?