Problem 1 A 1.5 kg uniform solid rod is hung by its end from the ceiling. When the rod is set into simple harmonic motion (I = m), it oscillates with a period of 2 s. What is the total length L of the rod? Problem 2 Consider a spring hung vertically from the ceiling. (a)When a small object with an inertia of 3kg is attached to the spring, the spring is stretched 0.15m. What is the force constant of the spring? (b)The 3kg object is removed and a different one attached to the spring. It then undergoes simple harmonic motion with a period of seconds. What is the inertia of the new object? (c) You pulled the object in part (b) so it undergoes simple harmonic motion with an amplitude of 10 cm. What is its maximum acceleration and velocity? (d)What is the total energy of the system? (e)Taking upward to be positive, when in the motion do the object's maximum amplitude, velocity and acceleration occur? (f)If we call the time where it is first passing through the equilibrium position on the way up t = 0, write an equation of motion for the object's oscillation, r(t) =?, identifying the values of all constants that you use.