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112. Problem 15.42 (RHK) There is an interesting relationship between the
block-spring system and the simple pendulum. Suppose that we hang an object of
mass M on the end of a spring, and when the object is in equilibrium the spring
is stretched a distance h. We have to show that the frequency of this
block-spring system is the sane as that of a simple pendulum of mass and length
h, even if
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Solution: Click For PDF Version When a block of mass M is hanged from the spring its length stretches by distance h determined by its force constant k,
When the mass M is pulled down by a distance x from its equilibrium position, it is pulled up by the spring with force k x and its equation of motion is
It is a SHM with angular frequency
Therefore the SHM of the mass M is equivalent to SHM of a simple
pendulum of length h with a bob of mass m. As the SHM of the
simple pendulum does not depend on the mass of the bob, above result holds even
if
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