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Consider a cylindrical sample of rubber, fixed at one end. It may be characterised by four state variables, but we are interested in only two, namely, temperature T (in K) and length L (in cm), the latter being varied through the application of some tensile/compressive force F. I It can be shown that, under certain conditions, T and L are related via the 1st order ODE dT dL T 10 (2-2-²) This equation assumes that the relaxed length of the cylinder is 1 cm i.e. L < 1 implies compression, while L> 1 implies extension,

Consider a cylindrical sample of rubber, fixed at one end. It may be characterised by four state variables, but we are interested in only two, namely, temperature T (in K) and length L (in cm), the latter being varied through the application of some tensile/compressive force F. I It can be shown that, under certain conditions, T and L are related via the 1st order ODE dT dL T 10 (2-2-²) This equation assumes that the relaxed length of the cylinder is 1 cm i.e. L < 1 implies compression, while L> 1 implies extension,

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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Use the initial condition T(1) = 300 to find the solution of the ODE
Consider a cylindrical sample of rubber, fixed at one end. It may be characterised by four state variables, but we are interested in only two, namely, temperature T (in K) and length L (in cm), the latter being varied through the application of some tensile/compressive force F. I F dT T 11 dL 10 It can be shown that, under certain conditions, T and L are related via the 1st order ODE L (L-L-²) This equation assumes that the relaxed length of the cylinder is 1 cm i.e. L < 1 implies compression, while L> 1 implies extension,
Transcribed Image Text:Consider a cylindrical sample of rubber, fixed at one end. It may be characterised by four state variables, but we are interested in only two, namely, temperature T (in K) and length L (in cm), the latter being varied through the application of some tensile/compressive force F. I F dT T 11 dL 10 It can be shown that, under certain conditions, T and L are related via the 1st order ODE L (L-L-²) This equation assumes that the relaxed length of the cylinder is 1 cm i.e. L < 1 implies compression, while L> 1 implies extension,
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