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A small cart of mass 0.8 kg is attached to one end of a massless, horizontal...

A small cart of mass 0.8 kg is attached to one end of a massless, horizontal spring as shown in the figure. The spring constant is 600 N/m. The spring is stretched by 0.05 m and the cart is released from rest. The cart then oscillates back and forth undergoing simple harmonic motion. Friction and air resistance are negligible.

a) (5 pts) Find the angular frequency ω of the motion.

b) (5 pts) How long does it take for the cart to complete one oscillation?

c) Find the maximum speed of the cart (5 pts). When the cart is moving with the speed, what is the displacement of the spring (1 pt)?

d) (8 pts) Find the total energy of the system.

e) (6 pts) Write the mathematical function that gives the position of the cart as a function of time. Take t = 0s to be the time the cart is released from rest. Your answer should contain only numbers (with units), trigonometric functions, and the independent variable t.

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