Solve Spring Oscillation: Find Max Speed & Kinetic Energy

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A 0.50 kg block attached to a spring with a spring constant of 80 N/m oscillates on a frictionless surface, with a total mechanical energy of 0.12 Joules. To find the maximum speed of the block, one must consider the conservation of mechanical energy, where all potential energy in the spring converts to kinetic energy at maximum speed. The relevant formulas include the potential energy of the spring, PE = (1/2)(k)(x^2), and kinetic energy, KE = (1/2)(m)(v^2). Understanding that the maximum speed occurs when all energy is kinetic is crucial for solving the problem. This discussion emphasizes the relationship between potential energy in the spring and kinetic energy of the block.
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1. A 0.50 Kilogram block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. The total mechanical energy 0.12 Joules. What is the greatest speed of the block. If somebody could just point me in the right direction, I'd appreciate it.



2. Fx=kx
Potential energy in a spring= (1/2)(k)(x2)



3. I don't even know where to start... I think just a little nudge should get me there though. This is our section for conservation of energy, so it's a good bet to think it has something to do with that.
 
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Conservation of mechanical energy. Does that help?
 
I need just a little more than that... I'm kind of slow when it comes to the recent portions of this course.
 
When it's asking for the greatest speed of the block, it's asking when is all of the energy of the block converted into kinetic energy?

What is the formula for kinetic energy?
 

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