Potential Energy problem (i think)

[nebbione]

Homework Statement

Write the cartesian equations of the movement of a material point of mass m that is in a forces field in which the potential energy is V(x,y,z)=-αy^2 , and you know that at time t=0 the point is in the position which has coordinates (0,0,Z0) with velocity v=V0*j

P.S: Sorry for my bad english but i had to translate it because it was an exercise of an exam at Mechanical Engineering at University of Bologna, Italy

Homework Equations

I can't understand how i can solvec this kind of prblem ? How should i think?
I heard that it's something with differental equations write ?

The Attempt at a Solution

Sincerely don't know where to start.

 

[vela]

When the problem asks for the equation of motion, it wants you to apply Newton's second law, F=ma.

 

[nebbione]

Thank you for the collaboration but sorry i don't have any idea on how to proceed to solve it! I know what are cartesian equations, i know what is potential energy but can't understand what the problem is asking me really and don't know how to proceed to solve it. Can you write the solution step by step ?

Thank you!

 

[vela]

No, that's not how it works here. I suggest you read the forum rules, particularly the section on homework help.

If you really are totally clueless and have absolutely no idea where to start, you're not at a point where you should be asking for help on this forum. You first need to go back to your book and notes, perhaps talk to your professor or teaching assistants, and get at least a minimal level of understanding so you can make a reasonable attempt at solving the problem.

 

[nebbione]

Ops sorry ! It won't happen again, I'm a new user anyway i don't have any idea on how to solve it... i'll try to ask one of my classmates.
Thank you!