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Damper Door Distance from wall Let the movement of the door after touching the soft closing device represented by a second order motion equation as in below: d²x dx m +C + kx dt Where,

Damper Door Distance from wall Let the movement of the door after touching the soft closing device represented by a second order motion equation as in below: d²x dx m +C + kx dt Where,

Advanced Engineering Mathematics
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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Spring Damper Door Distance from wall Let the movement of the door after touching the soft closing device represented by a second order motion equation as in below: d²x dx +C=+ kx dt m dt² Where, x is the distance of the door from the wall with x = 0 at the wall m is the mass of the door C is the damping capacity k is the spring constant Given the spring constant, k is 10 N/m, damping coefficient, C is 8 N s/m, mass of the door, m is 2 kg and the door is released from static at the distance from wall equal to 0.5 meter. i) Convert the given second-order equation in first order equations. ii) Identify all the initial or boundary conditions for the given system. ii) Suggest a first order accuracy numerical method to solve the first order equations derived in i). Hence, find the distance of x at t = 0.6 s using a step size of 0.2. iv) Given that the exact answer for x at t = 0.6 s is 0.29436 m, compare this with your answer in ii) by calculating the percentage error. Suggest two methods to improve the accuracy of the answer in i).
Transcribed Image Text:Spring Damper Door Distance from wall Let the movement of the door after touching the soft closing device represented by a second order motion equation as in below: d²x dx +C=+ kx dt m dt² Where, x is the distance of the door from the wall with x = 0 at the wall m is the mass of the door C is the damping capacity k is the spring constant Given the spring constant, k is 10 N/m, damping coefficient, C is 8 N s/m, mass of the door, m is 2 kg and the door is released from static at the distance from wall equal to 0.5 meter. i) Convert the given second-order equation in first order equations. ii) Identify all the initial or boundary conditions for the given system. ii) Suggest a first order accuracy numerical method to solve the first order equations derived in i). Hence, find the distance of x at t = 0.6 s using a step size of 0.2. iv) Given that the exact answer for x at t = 0.6 s is 0.29436 m, compare this with your answer in ii) by calculating the percentage error. Suggest two methods to improve the accuracy of the answer in i).
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