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A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position xo and initial velocity vo. Find the 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 form x(t)=C₁e Pl cos (@₁t-a). Also, find the undamped position function u(t)= Cocos (@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 (so c = 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). 1 m= n=₁ c = 4₁ k = 6₁ x₁ = 4₁ V₁ = 0 x(t)= which means the system is (1). (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or equal to 2x.) The undamped position is u(t)= (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or equal to 2x.) Choose the correct graph that compares x(t) and u(t). OA. O B. OC. Q Q Q MMA LA MAS 4. G (1) O underdamped. O critically damped. overdamped. Q

A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position xo and initial velocity vo. Find the 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 form x(t)=C₁e Pl cos (@₁t-a). Also, find the undamped position function u(t)= Cocos (@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 (so c = 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). 1 m= n=₁ c = 4₁ k = 6₁ x₁ = 4₁ V₁ = 0 x(t)= which means the system is (1). (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or equal to 2x.) The undamped position is u(t)= (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or equal to 2x.) Choose the correct graph that compares x(t) and u(t). OA. O B. OC. Q Q Q MMA LA MAS 4. G (1) O underdamped. O critically damped. overdamped. Q

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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2. A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position xo and initial velocity vo. Find the 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 form x(t)=C₁e Pt cos (@₁t-a₁). Also, find the undamped position function u(t)= Cocos (@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 (so c = 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). 1 m = 2, c = 4, k = 6, x₁ = 4, V₁ = 0 x(t) = which means the system is (1). (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or equal to 2x.) The undamped position is u(t)=[ (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or equal to 2.) Choose the correct graph that compares x(t) and u(t). O A. O B. Q M Catt 5 (1) O underdamped. O critically damped. O overdamped. OC. O D. Q Q MAS JA TAAS 2 3 Q G 12 iti W ibe ure
Transcribed Image Text:2. A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position xo and initial velocity vo. Find the 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 form x(t)=C₁e Pt cos (@₁t-a₁). Also, find the undamped position function u(t)= Cocos (@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 (so c = 0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). 1 m = 2, c = 4, k = 6, x₁ = 4, V₁ = 0 x(t) = which means the system is (1). (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or equal to 2x.) The undamped position is u(t)=[ (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than or equal to 2.) Choose the correct graph that compares x(t) and u(t). O A. O B. Q M Catt 5 (1) O underdamped. O critically damped. O overdamped. OC. O D. Q Q MAS JA TAAS 2 3 Q G 12 iti W ibe ure
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