What is the maximum length of the spring?

[annnnnw]

Homework Statement

A mass of 0.4 kg hangs motionless from a vertical spring whose length is 0.95 m and whose unstretched length is 0.65 m. Next, the mass is pulled down to where the spring has a length of 1.20 m and given an initial speed upwards of 1.6 m/s. What is the maximum length of the spring during the motion that follows?

Relevant Equations

Spring Stiffness F=kx
Conservation of energy

I know gravity needs to be taken into account and that I can find the stiffness but generally I'm pretty lost

 

[haruspex]

Any conservation laws that you can apply?

 

[annnnnw]

I tried
1/2(k_s)(s_f)^2 = 1/2(m)(v_i)^2 + 1/2(k_s)(s_i)^2

But I'm not really sure it's the best for what going on here

 

[berkeman]

Thread paused for Moderation...

 

[berkeman]

I tried
1/2(k_s)(s_f)^2 = 1/2(m)(v_i)^2 + 1/2(k_s)(s_i)^2

But I'm not really sure it's the best for what going on here

Thread is reopened provisionally.

@annnnnw -- Please show more effort in your replies in this thread. There are several types of energy involved in this question, including gravitational potential energy (GPE), kinetic energy (KE) and the spring's potential energy (PE) based on how extended it is from its resting postion. Please include all of these in your calculations. Thank you.