(a) The position of a mass in a spring-mass system is given as x(t) = 2cos4t. Find the period of oscillations and initial conditions. (b) Consider a vertical spring mass-damper-system with mass m = 2 kg, damping coefficient c = 5 N.s/m and stiffness k = 10 N/m. An external force f(t) = sin3t N is applied to the mass. (i) Find the static equilibrium position as measured from the un-stretched length of the spring (ii) Write the equation of motion. (iii) Find the natural and damped frequencies.

(a) The position of a mass in a spring-mass system is given as x(t) = 2cos4t. Find the period of oscillations and initial conditions. (b) Consider a vertical spring mass-damper-system with mass m = 2 kg, damping coefficient c = 5 N.s/m and stiffness k = 10 N/m. An external force f(t) = sin3t N is applied to the mass. (i) Find the static equilibrium position as measured from the un-stretched length of the spring (ii) Write the equation of motion. (iii) Find the natural and damped frequencies.

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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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

Task 1
(a) The position of a mass in a spring-mass system is given as x(t) = 2cos4t. Find the period
of oscillations and initial conditions.
(b) Consider a vertical spring mass-damper-system with mass m = 2 kg, damping coefficient
c = 5 N.s/m and stiffness k = 10 N/m. An external force f(t) = sin3t N is applied to the
mass.
(i) Find the static equilibrium position as measured from the un-stretched length of the spring
(ii) Write the equation of motion.
(iii) Find the natural and damped frequencies.
(iv) In steady state, find the time delay in seconds between the mass position and At).
(v) Find the steady state maximum acceleration.

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