Maximizing Displacement on an Incline for a Mass Attached to a Spring

[gunni91]

Homework Statement

The mass m is attached to a spring with spring constant k, on incline which forms
the angle α to the horizontal. The mass is stretched into the distance ℓ from the equilibrium position
the spring and kept there. How far up the incline can the mass go after
it is released, if friction is negligible?

Homework Equations

The Attempt at a Solution

 

[G01]

What have you tried so far?

You must show your own attempt at the problem if you want to get help here. Please see point 1 in the below post:

https://www.physicsforums.com/showthread.php?t=94380

Also, problems like this should be posted in the Introductory Physics subforum. Advanced physics is reserved for upper level undergraduate and graduate level problems.

 

[Cipherflak]

start with setting up all the forces working just as you release the spring. At first, the spring force F(x)=-kx, (x in the direction of the plane) will be greater than the projection of gravity, but as x gets smaller, gravity will win (or even the spring might contract and push back).

X-direction:
F = ma= -m*g*cos(theta) - k(-x)

agree so far?