An object with mass m = 1 kg is attached to a spring with spring constant k and a dashpot with c = 20- N m/s 1 The mass is set in motion with initial position xo = meters and v₁ = -6 meters/second. Solve the initial value problem x" + 20x' + 100x = 0, x(0) = ½ x² (0) = -6 to find the position function x (t) of the object t seconds after it is released. Find the undamped position function u(t) = C cos(wt - a) (where 0 ≤ α < 2n) that would result if the mass and spring were set in motion with the same initial position xo = and v=-6, but with the dashpot disconnected. In order words, solve the initial value problem u" + 100u = 0, u(0) = ½, u' (0) = -6 and write your answer in the form u(t) = C cos(wt - a), where 0 ≤ a < 2.
An object with mass m = 1 kg is attached to a spring with spring constant k and a dashpot with c = 20- N m/s 1 The mass is set in motion with initial position xo = meters and v₁ = -6 meters/second. Solve the initial value problem x" + 20x' + 100x = 0, x(0) = ½ x² (0) = -6 to find the position function x (t) of the object t seconds after it is released. Find the undamped position function u(t) = C cos(wt - a) (where 0 ≤ α < 2n) that would result if the mass and spring were set in motion with the same initial position xo = and v=-6, but with the dashpot disconnected. In order words, solve the initial value problem u" + 100u = 0, u(0) = ½, u' (0) = -6 and write your answer in the form u(t) = C cos(wt - a), where 0 ≤ a < 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:An object with mass m = 1 kg is attached to a spring with spring constant k and a dashpot with c = 20-
N
m/s
1
The mass is set in motion with initial position xo = meters and v₁ = -6 meters/second.
Solve the initial value problem x" + 20x' + 100x = 0, x(0) = ½ x² (0) = -6 to find
the position function x (t) of the object t seconds after it is released.
Find the undamped position function u(t) = C cos(wt - a) (where 0 ≤ α < 2n)
that would result if the mass and spring were set in motion with the same initial position xo =
and v=-6, but with the dashpot disconnected.
In order words, solve the initial value problem u" + 100u = 0, u(0) = ½,
u' (0) = -6 and write your answer in the form u(t) = C cos(wt - a), where 0 < a < 2.
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