# Simple Harmonic Motion of a Spring

So over the weekend my physics prof has assigned an assignment where one of the questions is as follows and here is my thought process:

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 9.9 cm below the initial position? (c) An object of mass 160 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?

However, upon inspecting this question I realize that the 22cm stretch is not my maximum amplitude, but rather the distance from my un-stretched spring. There for in order to calculate anything with the one piece of information given, I somehow need to calculate my max amplitude. But in order to do that I need the mass of the object or the spring constant. If anyone could help me out here starting out that would be great. I'm not looking for the answer straight up, but i just would appreciate it if someone could put me in the direction on how to solve the equation because me and my classmates are stumped.

jedishrfu
Mentor
what if the 22cm stretch is the maximum? can you solve it then?

Well could you not manipulate the formula x(t)=Xmcos(wt+∅)? I have been stuck on this question for hours now with no progress at all and am running out of motivation.

jedishrfu
Mentor
Im trying to say your assumption was wrong. When the object reached yi - 22cm the force of the spring was enough to counteract gravity and so the object begins to go back up to the yi position and will oscillate between the two positions.

Dont forget that PF rules say you must follow the homework template and show some work before we can help further.