Mass attached to vertical spring

AI Thread Summary
An object with a mass of 0.4 kg is attached to a horizontal spring with a spring constant of 80 N/m and is displaced 0.1 m from its equilibrium position. When released from rest, it undergoes simple harmonic motion, and the task is to find its velocity at the equilibrium point. The calculated velocity is 0.7 m/s, but the solution key indicates it should be 1.4 m/s, referencing Serway's Physics. To resolve the discrepancy, a free body diagram is suggested, along with applying Newton's second law to analyze the motion. The initial conditions can then be used to derive the position and velocity functions over time.
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Homework Statement



an object of mass 0.4kg is attached to horizontal spring of ,,spring constant 80N/m,,and it is displaced 0.1m from equilibrium postion and released from rest,,such that it perform up and down simple harmonic motion.find its velocity when it passes through equilibrium point

Homework Equations



k.e=kinetic energy...k.e=0.5><(mg)^2/k...

3. The attemp at a solution
solving above equation will give,,v=0.7,,,but in solution key it is 1.4m/s ref(serway physics vol 8..ch#13,pg451,,ques,4
 
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Sketch a free body diagram for the mass and write NII for its motion. Then use the initial conditions to find the position of the mass as a function of t, from which you can obtain its velocity as a function of t.
 

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