Q4.A damped spring, constrained to move in one direction, such as might be found in a railway buffer, is subjected to an unit impulse of duration 5 seconds. The spring constant divided by the mass causing the impulse is 10m-2s-2 and the frictional force divided by this mass is 2m-2s-2. (a) Write down the equation governing the motion in terms of the displacement r. (b) Write down the initial conditions on the displacement æ(0) and velocity a'(0). (c) Solve the equation for the displacement r(t) as a function of time. (d) What is æ(r)? 1+e=* b) 1+ e-2# 1-e-2 d) 10 10 20 20

Q4.A damped spring, constrained to move in one direction, such as might be found in a railway buffer, is subjected to an unit impulse of duration 5 seconds. The spring constant divided by the mass causing the impulse is 10m-2s-2 and the frictional force divided by this mass is 2m-2s-2. (a) Write down the equation governing the motion in terms of the displacement r. (b) Write down the initial conditions on the displacement æ(0) and velocity a'(0). (c) Solve the equation for the displacement r(t) as a function of time. (d) What is æ(r)? 1+e=* b) 1+ e-2# 1-e-2 d) 10 10 20 20

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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Question

Q4.A damped spring, constrained to move in one direction, such as might be found in a railway buffer, is
subjected to an unit impulse of duration 5 seconds. The spring constant divided by the mass causing the
impulse is 10m-2s-2 and the frictional force divided by this mass is 2m-2s-2.
(a) Write down the equation governing the motion in terms of the displacement r.
(b) Write down the initial conditions on the displacement æ(0) and velocity r'(0).
(c) Solve the equation for the displacement r(t) as a function of time.
(d) What is r(1)?
1+e-27
c)
-2x
1-e-T
b)
1+e-*
a)
1-e
d)
10
10
20
20

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