A simple pendulum of length ' = 0.35m has a mass m = 0.24kg attached to the end. The pendulum is pulled to an angle ₀ = 10 from the vertical and is then released at t = 0. (a)Find the equation of the form = Acos(t + ) for the motion of the pendulum, filling in whatever numbers you can for the variables in the equation. (b) Use your equation above to find an equation for the angular velocity d/dt of the pendulum over time, again plugging in numbers where you can. What is the maximum angular velocity of the pendulum in rad/s? (c) Determine an expression for the linear velocity v of the pendulum mass as a function of time. What is the maximum linear velocity of the mass in m/s?

(d) Determine an expression for the kinetic energy K of the pendulum mass as a function of time. What is the maximum kinetic energy of the pendulum in J? (e) Check to see if mechanical energy is conserved for the pendulum by calculating the maximum gravitational potential energy U _g it obtains during its oscillations Hint: what is the angular velocity and position of the pendulum when the potential energy is maximized?