- #1
lonewolf5999
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Consider a mass hanging freely from a spring, oriented vertically downwards. We know that because the restoring force acting on the mass is directly proportional to the displacement of the mass from the equilibrium position, i.e. the extension of the spring (F=kx), the system exhibits simple harmonic motion.
Suppose that we pull it down by a distance of a from its equilibrium position, and then release it. Using energy considerations, and letting b be the maximum displacement of the mass from the equilibrium position during the upward portion of its motion,
(1/2)ka2 - mga = (1/2)kb2 + mgb, and solving,
a - b = 2mg/k
So, a must be greater than b.
Is this analysis correct, and if so, does this mean that systems executing SHM need not have equal amplitudes in the different oscillation directions? (e.g. during the upward motion, its amplitude is different from that of its downward motion)
Suppose that we pull it down by a distance of a from its equilibrium position, and then release it. Using energy considerations, and letting b be the maximum displacement of the mass from the equilibrium position during the upward portion of its motion,
(1/2)ka2 - mga = (1/2)kb2 + mgb, and solving,
a - b = 2mg/k
So, a must be greater than b.
Is this analysis correct, and if so, does this mean that systems executing SHM need not have equal amplitudes in the different oscillation directions? (e.g. during the upward motion, its amplitude is different from that of its downward motion)