A mass-spring system of mass m = 0.2 kg and elastic constant k = 5 N/m is immersed in a viscous fluid which exerts a damping force on the system. Furthermore, the system is subjected to a harmonic forcing of intensity F_0 = 10 N and frequency w rad/s. The value of the damping constant is b = 1.5 Ns/m. If the system starts at rest and in its equilibrium position, find: a) the frequency w for which the system is in resonance; b) Make a graph of position v/s time where the amplitude and period of the system can be seen explicitly if the frequency w is equal to twice the resonance frequency; c) Make a graph of amplitude v/s frequency where the maximum frequency and the resonance frequency of the system can be seen explicitly.
A mass-spring system of mass m = 0.2 kg and elastic constant k = 5 N/m is immersed in a viscous fluid which exerts a damping force on the system. Furthermore, the system is subjected to a harmonic forcing of intensity F_0 = 10 N and frequency w rad/s. The value of the damping constant is b = 1.5 Ns/m. If the system starts at rest and in its equilibrium position, find: a) the frequency w for which the system is in resonance; b) Make a graph of position v/s time where the amplitude and period of the system can be seen explicitly if the frequency w is equal to twice the resonance frequency; c) Make a graph of amplitude v/s frequency where the maximum frequency and the resonance frequency of the system can be seen explicitly.
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 mass-spring system of mass m = 0.2 kg and elastic constant k = 5 N/m is immersed in a viscous fluid which exerts a damping force on the system. Furthermore, the system is subjected to a harmonic forcing of intensity F_0 = 10 N and frequency w rad/s. The value of the damping constant is b = 1.5 Ns/m. If the system starts at rest and in its equilibrium position, find:
a) the frequency w for which the system is in resonance;
b) Make a graph of position v/s time where the amplitude and period of the system can be seen explicitly if the frequency w is equal to twice the resonance frequency;
c) Make a graph of amplitude v/s frequency where the maximum frequency and the resonance frequency of the system can be seen explicitly.
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