Challenge Problem #3: Damped Periodic Motion
If there is no friction in the setup shown below, the block, once it is released, will oscillate
forever between the two springs. Its motion could be described as simple periodic or
simple harmonic motion.
If there is friction, however, mechanical energy will gradually be lost to heat and the
oscillations will get smaller and smaller until eventually the block comes to rest. In this
case the motion would be called damped periodic motion. If the oscillations die out very
rapidly (for example, over only a few oscillations) we would call it heavily damped
periodic motion.
Given the values shown below, determine where the point P (mid-point of block) will be
with respect to the mid-point of the table when the oscillations die out and the block comes
to rest. Assume both springs are identical.
Spring constant: 152 N/m
Mass of block: 0.785 kg
Width of block: 6.00 cm
Coefficient of kinetic (and static) friction: 0.084
Mid-point of table
17.8 cm
Mid-point of table
12.0 cm
Block ready to be released
Both springs in rest positions
Left spring compressed;
P
17.8 cm
2007-08-27
22:48:24
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2 answers
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asked by
yusuke_kousuke
2