Energy conservation in oscillatory motion

AI Thread Summary
The discussion focuses on solving a physics problem involving energy conservation in oscillatory motion with a mass-spring system. A 0.321-kg mass attached to a spring with a force constant of 13.3 N/m is analyzed after being displaced 0.256 m from equilibrium. The correct speed of the mass when it is 0.128 m from equilibrium is determined to be 1.43 m/s. Participants emphasize the importance of equating the mechanical energies (potential and kinetic) at different states to find the unknowns. The approach involves calculating the initial and final energies and ensuring they are equal to solve for the speed.
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Homework Statement



A 0.321-kg mass is attached to a spring with a force constant of 13.3 N/m. If the mass is displaced .256 m grom the equilibrium and released, what is its speed when it is .128 m from equilibrium. The answer is 1.43 m/s

Homework Equations



k=(w^2)m
w=2pi/T

The Attempt at a Solution


I used the formula (1/2)mv^2= (1/2)kd^2. I solved for k and got 6.44 rad/s and then i solved the equation for v. I then used .128 for my d. I plugged in my answer and got 8.24. I also used d as .256 and got 1.64
 
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k is given as 13.3

here's how energy conservation works

for one state of system ... write all mechanical (potential + kinetic) energies associated with it
the do same for other state
the 2 energies shall be same so equate them and find unknown

so here find energy when spring is initially stretched and when it has extension .128 and equate them
 
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