Halliday, Resnick & Walker — Oscillations: Problem 17

17 A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position \( y_i \) such that the spring is at its rest length. The object is then released from \( y_i \) and oscillates up and down, with its lowest position being 10 cm below \( y_i \). (a) What is the frequency of the oscillation? (b) What is the speed of the object when it is 8.0 cm below the initial position? (c) An object of mass 600 g is attached to the first object, after which the system oscillates with half the original frequency. What is the mass of the first object? (d) How far below \( y_i \) is the new equilibrium (rest) position with both objects attached to the spring?