Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
d²y dy dt² dt +c- Dirac delta function and F m- = -mg + Fod(t-1) in the 1. CUL

d²y dy dt² dt +c- Dirac delta function and F m- = -mg + Fod(t-1) in the 1. CUL

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
See similar textbooks
Question
You do not need to show work for decomposing partial fractions
Ps) Consider a tennis ball falling in a vertical direction, subject to gravitational force and air resistance, described by the second-order differential equation (0.1) where m is the mass of the object, c is the friction coefficient, y(t) represents the height of the object above the reference point y = 0 which is the ground and g is the acceleration due to gravity. Additionally, the ball is released from rest at an initial height, that is y(0) = yo > 0, and with an initial velocity of zero, that is y' (0) = 0. (b) 401 para y (0) char no 0. m d²y dy + c dt² dt m = -mg for the uni Note that the limit as t goes to intim Now, a tennis player is going to hit (perfectly vertically) the tennis ball u ward at t = 1, incorporating an impulse in the ODE as follows dy d²y + c dt² dt 2011 = -mg + Fod(t-1) Ad on a well as the (0.2) where 8(t) is the Dirac delta function and Fo≥ 0 is the strength of the impulse. Use the Laplace transform to solve (0.2) with initial conditions y(0) = yo and y' (0) = 0. Your solution y(t) should depend on t as well as the parameters m, c, g, yo and Fo.
Transcribed Image Text:Ps) Consider a tennis ball falling in a vertical direction, subject to gravitational force and air resistance, described by the second-order differential equation (0.1) where m is the mass of the object, c is the friction coefficient, y(t) represents the height of the object above the reference point y = 0 which is the ground and g is the acceleration due to gravity. Additionally, the ball is released from rest at an initial height, that is y(0) = yo > 0, and with an initial velocity of zero, that is y' (0) = 0. (b) 401 para y (0) char no 0. m d²y dy + c dt² dt m = -mg for the uni Note that the limit as t goes to intim Now, a tennis player is going to hit (perfectly vertically) the tennis ball u ward at t = 1, incorporating an impulse in the ODE as follows dy d²y + c dt² dt 2011 = -mg + Fod(t-1) Ad on a well as the (0.2) where 8(t) is the Dirac delta function and Fo≥ 0 is the strength of the impulse. Use the Laplace transform to solve (0.2) with initial conditions y(0) = yo and y' (0) = 0. Your solution y(t) should depend on t as well as the parameters m, c, g, yo and Fo.
Expert Solution
steps

Step by step

Solved in 6 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS