A massless spring hangs from the ceiling with a small object attached to its low

Question

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 yi such that the spring is at its rest length. The object is then released from yi and oscillates up and down, with its lowest position being 22 cm below yi. (a) What is the frequency (in Hz) of the oscillation? (b) What is the speed of the object when it is 15 cm below the initial position? (c) An object of mass 250 g is attached to the first object, after which the system oscillates with half the original frequency. What is the mass (in kg) of the first object? (d) How far below yi is the new equilibrium (rest) position with both objects attached to the sping?

Explanation / Answer

There appears to be some missing data, is there a second object? f=(k/m)^(1/2)/(2 pi) m v^2 = k (A sin(2 pi f t))^2 y = A cos(2 pi f t) if we call the time it is at it's lowest point t=0 first equation will give k from 2nd equation we derive the relation between A (max displacement from final equilibrium) and t then 3rd equation gives y

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