Energy in SHM
المؤلف:
Professor John W. Norbury
المصدر:
ELEMENTARY MECHANICS & THERMODYNAMICS
الجزء والصفحة:
p 181
30-12-2016
2780
Energy in SHM
We found before that the potential energy stored in a spring is 
and the kinetic energy is 
. The conservation of mechanical energy says that
where the total energy is
That is
Thus E is constant. However for a spring x and v are always changing. Can we be sure that E is always constant ?
Example For SHM, show that the total energy is always constant even though K and U always change.
Solution Recall that for SHM we have x = xm cos 
t and v = -xm sin t. Thus
and
Thus U and K always change. Let's add them.
but we previously found that 
giving
which is always constant because the amplitude xm is constant!
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