Equation 2 (M) is a second order differential equation that models the relationship between the input force Fin being applied to a shock absorber system and the shock absorber spring displacement ‘x'. (i) Assuming ALL initial conditions are zero and using the constants below, solve the second order differential equation given in equation 2 (M). Use Laplace Transforms. The input is a step of 2 N. (ii) The friction constant within the dashpot has been reduced by a factor of 4. Again using Laplace Transfroms, solve the equation and comment on the results. (iii) Calculate the value of friction constant that will give a critically damped response.

Equation 2 (M) is a second order differential equation that models the relationship between the input force Fin being applied to a shock absorber system and the shock absorber spring displacement ‘x'. (i) Assuming ALL initial conditions are zero and using the constants below, solve the second order differential equation given in equation 2 (M). Use Laplace Transforms. The input is a step of 2 N. (ii) The friction constant within the dashpot has been reduced by a factor of 4. Again using Laplace Transfroms, solve the equation and comment on the results. (iii) Calculate the value of friction constant that will give a critically damped response.

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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Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

d²x
dt²
Fin = m-
dx
+Ka +K₂x
dt
m =
- Equation 2 (M)
Equation 2 (M) is a second order differential equation that models the relationship between the input force
Fin being applied to a shock absorber system and the shock absorber spring displacement 'x'.
(i) Assuming ALL initial conditions are zero and using the constants below, solve the second order
differential equation given in equation 2 (M). Use Laplace Transforms. The input is a step of 2
N.
(ii) The friction constant within the dashpot has been reduced by a factor of 4. Again using Laplace
Transfroms, solve the equation and comment on the results.
(iii)
Calculate the value of friction constant that will give a critically damped response.
10 kg, Ka= 50 N/m/s, K, = 80 N/m

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