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The displacement x(t) cms at time t seconds, of a spring moving along a line is given by the formula: x(t) = 8e- cos(2t). Compute the velocity x'(t) and acceleration x"(t) of the spring and show that these are related by a formula of the kind x" + ax' + bx = 0 for suitable constants a and b which must be found. Also estimate the maximum speed of the particle and its maximum acceleration, during its motion, with explanation. Also discuss the behavior of the motion for large times.

The displacement x(t) cms at time t seconds, of a spring moving along a line is given by the formula: x(t) = 8e- cos(2t). Compute the velocity x'(t) and acceleration x"(t) of the spring and show that these are related by a formula of the kind x" + ax' + bx = 0 for suitable constants a and b which must be found. Also estimate the maximum speed of the particle and its maximum acceleration, during its motion, with explanation. Also discuss the behavior of the motion for large times.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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The displacement x(t) cms at time t seconds, of a spring moving along a line is given by the formula: x(t) 3D80' cos(2t). Compute the velocity x'(t) and acceleration x"(t) of the spring and show that these are related by a formula of the kind x" + ax' + bx = 0 for suitable constants a and b which must be found. Also estimate the maximum speed of the particle and its maximum acceleration, during its motion, with explanation. Also discuss the behavior of the motion for large times.
Transcribed Image Text:The displacement x(t) cms at time t seconds, of a spring moving along a line is given by the formula: x(t) 3D80' cos(2t). Compute the velocity x'(t) and acceleration x"(t) of the spring and show that these are related by a formula of the kind x" + ax' + bx = 0 for suitable constants a and b which must be found. Also estimate the maximum speed of the particle and its maximum acceleration, during its motion, with explanation. Also discuss the behavior of the motion for large times.
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