Calculating Spring Constant and Properties of Simple Harmonic Motion

[ick24]

Homework Statement

A vertical spring, fixed at the upper end, has a mass attached to the lower end. When the
spring is given a small extension it was observed to oscillate at a rate of 45 cycles per
minute. When an additional 160g mass is attached to the spring, it oscillated at a rate of
25 cycles per minute. Calculate the spring constant.
(i) If the spring is then given a deflection of 12cm, what will be the Potential energy
stored in the system.
(ii) What is velocity of the mass as it passes the equilibrium point?
(iii) What is the maximum acceleration of the mass?
(iv) What is the velocity of the mass at a distance of 8cm from the equilibrium point?
(v) Calculate the displacement at a time t= 0.5 second.

Homework Equations

mg=-kx

The Attempt at a Solution

tried to figure out how to find the constant (k)
i don't see x and i don't know how to find the constant

 

[Filip Larsen]

You should probably try see if you can find some relevant equations in your textbook that relates the spring constant to the angular speed and mass load.