Question

S11. Suppose that the mass in a spring-mass-dashpot system with m = 1, c = 2, and k = 8 is set in motion (at t = 0) with x(0) = 0 and x'(0) = √7. When x(t) > 0 the spring is stretched, and the spring is compressed when x(t) < 0. a) Find the position of the mass for all t > 0. b) Even though the motion is not periodic, show that the mass passes through the equilibrium position every π/√7 seconds (which is half the "pseudo-period").

Name: s11 suppose that the mass in a spring mass dashpot system with m 1 c 2 and k 8 is set in motion at t 0 with x0 0 and x0 7 when xt 0 the spring is stretched and the spring is compressed when 13558
Uploaded: 2021-12-22T15:11:33-08:00
Duration: 41 s
Channel: Hast Aggarwal
Description: s11 suppose that the mass in a spring mass dashpot system with m 1 c 2 and k 8 is set in motion at t 0 with x0 0 and x0 7 when xt 0 the spring is stretched and the spring is compressed when 13558

          S11. Suppose that the mass in a spring-mass-dashpot system with m = 1, c = 2, and k = 8 is set in motion (at t = 0) with x(0) = 0 and x'(0) = √7. When x(t) > 0 the spring is stretched, and the spring is compressed when x(t) < 0.
a) Find the position of the mass for all t > 0.
b) Even though the motion is not periodic, show that the mass passes through the equilibrium position every π/√7 seconds (which is half the "pseudo-period").

s11 suppose that the mass in a spring mass dashpot system with m 1 c 2 and k 8 is set in motion at t 0 with x0 0 and x0 7 when xt 0 the spring is stretched and the spring is compressed when 13558

Added by Kayla M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Hast Aggarwal

12/22/2021

Step 1

The characteristic equation is r^2 + 2r + 8 = 0. Solving this quadratic equation, we get r = -1 ± 3i. Therefore, the general solution is x(t) = e^(-t) (Acos(3t) + Bsin(3t)). Show more…

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S11. Suppose that the mass in a spring-mass-dashpot system with m = 1, c = 2, and k = 8 is set in motion (at t = 0) with x(0) = 0 and x'(0) = √7. When x(t) > 0 the spring is stretched, and the spring is compressed when x(t) < 0. a) Find the position of the mass for all t > 0. b) Even though the motion is not periodic, show that the mass passes through the equilibrium position every π/√7 seconds (which is half the "pseudo-period").