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Problem 8: ( A 0.5 kg mass stretches a spring .098 m. The mass starts from equilibrium with the downward velocity of 16 m/s and the subsequent motion takes place in a medium that offers a damping force numerically equal to 6 times the instantaneous velocity. Assuming that the gravitational acceleration is 9.8 m/s?, find the position of the mass at any time t >0.

Problem 8: ( A 0.5 kg mass stretches a spring .098 m. The mass starts from equilibrium with the downward velocity of 16 m/s and the subsequent motion takes place in a medium that offers a damping force numerically equal to 6 times the instantaneous velocity. Assuming that the gravitational acceleration is 9.8 m/s?, find the position of the mass at any time t >0.

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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TABLE OF LAPLACE TRANSFORMS L{1} n! L{t"} sn+1 L {sin (at)} s2 + a? L{cos (at)} s2 + a? 1 S - a L{d(t – a)} L{f(t)8(t – a)} f(a)e-as F(s – a) s"Y (s) – s"-'y(0) – ...- y(n-1)(0) L{f * g} F(s) G(s) -as L{U (t – a)} L{f(t – a)U (t – a)} e-a* F(s) MISCELLANEOUS FORMULAS yıf %3D W W Y2 Yn ... W = (n) (n) (n) Yn ...
Transcribed Image Text:TABLE OF LAPLACE TRANSFORMS L{1} n! L{t"} sn+1 L {sin (at)} s2 + a? L{cos (at)} s2 + a? 1 S - a L{d(t – a)} L{f(t)8(t – a)} f(a)e-as F(s – a) s"Y (s) – s"-'y(0) – ...- y(n-1)(0) L{f * g} F(s) G(s) -as L{U (t – a)} L{f(t – a)U (t – a)} e-a* F(s) MISCELLANEOUS FORMULAS yıf %3D W W Y2 Yn ... W = (n) (n) (n) Yn ...
Problem 8: ( A 0.5 kg mass stretches a spring .098 m. The mass starts from equilibrium with the downward velocity of 16 m/s and the subsequent motion takes place in a medium that offers a damping force numerically equal to 6 times the instantaneous velocity. Assuming that the gravitational acceleration is 9.8 m/s?, find the position of the mass at any time t > 0.
Transcribed Image Text:Problem 8: ( A 0.5 kg mass stretches a spring .098 m. The mass starts from equilibrium with the downward velocity of 16 m/s and the subsequent motion takes place in a medium that offers a damping force numerically equal to 6 times the instantaneous velocity. Assuming that the gravitational acceleration is 9.8 m/s?, find the position of the mass at any time t > 0.
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