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A spring which stretches by an amount e under a force mi'e is suspended from a support O and has a mass m at the lower end. Initially the mass is at rest in its equilibrium position at a point A below O. A vertical oscillation is now given to the support O such that at any time (t > 0) its displacement below'its initial position is a sin nt. Show that the displacement x of the mass below A is given by d²x/dt2 + 2?x =X²a sin nt. Hence show that if n +1, the displacement is given by x = ha (A sin nt – n sin At)/(x² - n). What happens when n =1?

A spring which stretches by an amount e under a force mi'e is suspended from a support O and has a mass m at the lower end. Initially the mass is at rest in its equilibrium position at a point A below O. A vertical oscillation is now given to the support O such that at any time (t > 0) its displacement below'its initial position is a sin nt. Show that the displacement x of the mass below A is given by d²x/dt2 + 2?x =X²a sin nt. Hence show that if n +1, the displacement is given by x = ha (A sin nt – n sin At)/(x² - n). What happens when n =1?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A spring which stretches by an amount e under a force mke is suspended from a support 0 and has a mass m at the lower end. Initially the mass is at rest in its equilibrium position at a point A below O. A vertical oscillation is now given to the support O such that at any time (t > 0) its displacement below'its initial position is a sin nt. Show that the displacement x of the mass below A is given by d²x/dt2 + 2x = 2²a sin nt. Hence show that if n + 1, the displacement is given by x = ha (A sin nt – n sin At)/(x² - n). What happens when n =
Transcribed Image Text:A spring which stretches by an amount e under a force mke is suspended from a support 0 and has a mass m at the lower end. Initially the mass is at rest in its equilibrium position at a point A below O. A vertical oscillation is now given to the support O such that at any time (t > 0) its displacement below'its initial position is a sin nt. Show that the displacement x of the mass below A is given by d²x/dt2 + 2x = 2²a sin nt. Hence show that if n + 1, the displacement is given by x = ha (A sin nt – n sin At)/(x² - n). What happens when n =
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