Explanation Given data: The function x ( t ) = e − t cos t is the solution of the differential equation d 2 x d t 2 = − 2 x − 2 d x d t . Method/Formula used: We use graphing calculator to graph the given function. Calculation: A spring − mass system (spring constant k ) is shown in figure here. The mass in motion moves on a rough surface possessing friction. Let a mass mattached to spring is displaced through a distance x , and then released that set spring mass system in motion. At any time t the forces acting on the mass are: (i) Restoring force directly proportional to the displacement, f 1 = − k x , and (ii) force of friction or damping force which is directly proportional to the velocity v of the mass, i.e., force = f 2 = − q v , where q is a constant. Thus, net force on the mass in motion is F = f 1 + f 2 = − k x − q d x d t . Therefore, by Newton’s law of motion F = mass×acceleration = m d 2 x d t

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

3rd Edition

ISBN: 9780840064189

Author: Frederick R. Adler

Publisher: Cengage Learning

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Chapter 2.10, Problem 40E

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To graph: The solution of differential equation d2xdt2=−2x−2dxdt .The function x(t)=e−tcost is the solution of the differential equation d2xdt2=−2x−2dxdt , each term has its own meaning whose explanation to be given.

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Chapter 2.10, Problem 39E

Chapter 2.10, Problem 41E

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Chapter 2 Solutions

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

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To graph: The solution of differential equation d 2 x d t 2 = − 2 x − 2 d x d t .The function x ( t ) = e − t cos t is the solution of the differential equation d 2 x d t 2 = − 2 x − 2 d x d t , each term has its own meaning whose explanation to be given.

Solution Summary: The author explains how to graph the given function using a graphing calculator.

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To graph: The solution of differential equation d2xdt2=−2x−2dxdt .The function x(t)=e−tcost is the solution of the differential equation d2xdt2=−2x−2dxdt , each term has its own meaning whose explanation to be given.

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