An Atwood machine has masses m₁ and m₂ (m₂ > m₁) connected by an ideal rope of length ℓ of negligible mass through a pulley of radius r with negligible mass and frictionless. Determine:
a) The acceleration of the system as a function of time;
b) The speed of the system as a function of time;
c) The equation of motion as a function of time.

A body of mass m is attached to the end of a spring with constant k, resting on a horizontal frictionless surface. The other end of the spring is fixed at a wall. The body is moved away from the equilibrium position, and the body is released. Determine the equation of motion of the body.