1) Guess the form and solve for the particular solution of a driven oscillator described by the equation: mx" + cx' + kx = Fosin(at) 2) A mass of 4 kg on a spring with k = 4 N/m and a damping constant c = 1Ns/m is driven by a force following the function Focos(cat); where FO=2 N. Find the driving frequency that causes practical resonance and find the amplitude. 3) Suppose there is no damping in a mass and spring system with m = 5, k = 20, and Fo= 5. Suppose wis chosen to be precisely the resonance frequency. a) Find a b) Find the amplitude of the oscillations at time = 100, given that the system is at rest at r=0.
1) Guess the form and solve for the particular solution of a driven oscillator described by the equation: mx" + cx' + kx = Fosin(at) 2) A mass of 4 kg on a spring with k = 4 N/m and a damping constant c = 1Ns/m is driven by a force following the function Focos(cat); where FO=2 N. Find the driving frequency that causes practical resonance and find the amplitude. 3) Suppose there is no damping in a mass and spring system with m = 5, k = 20, and Fo= 5. Suppose wis chosen to be precisely the resonance frequency. a) Find a b) Find the amplitude of the oscillations at time = 100, given that the system is at rest at r=0.
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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![1) Guess the form and solve for the particular solution of a driven oscillator described
by the equation:
mx" + cx' + kx = Fosin(wt)
2) A mass of 4 kg on a spring with k = 4 N/m and a damping constant c = 1Ns/m is
driven by a force following the function Focos(at); where FO = 2 N. Find the driving
frequency that causes practical resonance and find the amplitude.
3) Suppose there is no damping in a mass and spring system with m = 5, k = 20,
and Fo= 5. Suppose is chosen to be precisely the resonance frequency.
a) Find a
b) Find the amplitude of the oscillations at time = 100, given that the system is at rest
at / = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd096848c-806f-423f-824a-70f6a412600a%2Fc0d33f7e-c98a-4ca9-8a70-c3a1077ca6ff%2Fh6izkje_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1) Guess the form and solve for the particular solution of a driven oscillator described
by the equation:
mx" + cx' + kx = Fosin(wt)
2) A mass of 4 kg on a spring with k = 4 N/m and a damping constant c = 1Ns/m is
driven by a force following the function Focos(at); where FO = 2 N. Find the driving
frequency that causes practical resonance and find the amplitude.
3) Suppose there is no damping in a mass and spring system with m = 5, k = 20,
and Fo= 5. Suppose is chosen to be precisely the resonance frequency.
a) Find a
b) Find the amplitude of the oscillations at time = 100, given that the system is at rest
at / = 0.
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