Where does the energy go? need help

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Tinamuline

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where does the energy go at the end?

When a mass is hanged to the end of a spring, and let it down. The loss in P.E. of the mass is mgx, where x is the extension. Whereas, the energy stored in the spring by Hooke's law is 1/2(k)(x)^2 = 1/2(F)(x) = 1/2(mg)(x). Why the energy loss by the mass is not equal to the energy gained by the spring? where does the energy go? Please help and give me the answer. Thank you.
 

where does energy go in a damped spring

Are you considering the X value correctly ?
The x value must be considered from the whole cicle and not half of the cicle.
 

The other part of the energy is from the velocity of the mass in a free situation.

You seem to be visualizing the situation where your hand is under the mass as it is lowered. Your hand absorbs some of the energy.
 

Thank you for replying. However, I am still wandering why my hand absorbs part of the energy of the system, cos' I just let the mass fall slowly. May be you are right. Please explain further. Thank you.
 

Your hand exerts a force as it travels a distance. Work = force x distance.
 

LEt us do the experiemnt by hanging the spring to the ceiling.Now when the mass falls by a distance and finally comes to rest after oscillations.If x is the stretch in the spring ,then energy stored in the spring is (1/2)*k*(x^2);
This is not equal to the PE lost by the mass which is mgx,because before coming to rest from oscilations,the mass would have extended further than x and the frictional resistance of air around it works to stop these oscillations.So the unequalness in the energies is due to the energy lost in these damped oscillations.
I think I did not confuse you.
 

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