5. A mass m is attached to both a spring (with given spring constant k) and a dashpot (with damping constant c). The mass is set in motion with initial position x, and velocity vo. A) Find the damped position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the formx(t) = c,e=pt cos(w¡t – az) B) Find the undamped function u(t) = C9e¯pt cos(wot – ao) that would result if the mass on the spring were set in motion with the same initial position and velocity but with the dashpot disconnected. m = 3, c = 30, k = 63, xo = 2, vo = 2

5. A mass m is attached to both a spring (with given spring constant k) and a dashpot (with damping constant c). The mass is set in motion with initial position x, and velocity vo. A) Find the damped position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the formx(t) = c,e=pt cos(w¡t – az) B) Find the undamped function u(t) = C9e¯pt cos(wot – ao) that would result if the mass on the spring were set in motion with the same initial position and velocity but with the dashpot disconnected. m = 3, c = 30, k = 63, xo = 2, vo = 2

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

5. A mass m is attached to both a spring (with given spring constant k) and a dashpot (with
damping constant c). The mass is set in motion with initial position xo and velocity vo.
A) Find the damped position function x(t) and determine whether the motion is overdamped,
critically damped, or underdamped. If it is underdamped, write the position function in the
formx(t) = ce¬pt cos(wit – a1)
B) Find the undamped function u(t) = coe-pt cos(@ot – ao) that would result if the mass on the
spring were set in motion with the same initial position and velocity but with the dashpot
disconnected.
m = 3, c = 30, k = 63, xo = 2, vo = 2

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