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) = C₁ e pt cos (@₁t-α₁). Also, find the undamped position function u(t)= Cocos (@ot-xo) 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= = ₁ , c= 3, k= 8, x₁ = 6, Vo = 0 C= x(t) = which means the system is (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.)
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) = C₁ e pt cos (@₁t-α₁). Also, find the undamped position function u(t)= Cocos (@ot-xo) 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= = ₁ , c= 3, k= 8, x₁ = 6, Vo = 0 C= x(t) = which means the system is (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.)
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Please help ASAP! Need to find x(t) and u(t) both.
Need only a handwritten solution only (not a typed one).
Transcribed Image Text: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
X 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-α₁). Also, find the undamped position function u(t) = ₁ cos (@txo) 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
4₁ c = 3, k = 8₁ x₁ = 6, v₁ = 0
8,
m=-
x(t) =, which means the system is
(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 2à.)
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