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
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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
Transcribed Image Text: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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