Solve Inclined Plane System with Spring & Mass

[Pyae]

Homework Statement

an inclined plane of angle 20 degrees has aspring of force constant k=500 N/m fastened securely at the bottomso that the spring is parallel to the surface. a block of massm=2.50kg is placed on the plane at a distance d=0.300m from thespring. from this position, the block is projected downward towardthe spring with a speed v=0.750 m/s. by what distance is the springcompressed when the block momentarily comes to rest?

Homework Equations

F = kx and F = ma

The Attempt at a Solution

The book says the answer is 0.131 m. But I get different answer. Here's what I'm doing.
a = g * sinθ

m * ax = k * x

Can someone please help me??

 

[collinsmark]

The book says the answer is 0.131 m. But I get different answer. Here's what I'm doing.
a = g * sinθ

m * ax = k * x

Your attempted approach might work if the system was in a state of static equilibrium, but it's not. Even though the instantaneous velocity of the block is zero, it is accelerating and that makes a big difference.

I suggest using conservation of energy to solve this problem (you could use kinematics to solve it, but I think conservation of energy will be a little easier).