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8 3. For a free fall problem, problem, y yo(t-0) ygr- 0 is not obvious, it...
1. A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high...
1. A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise? (b) How long does it take to reach its highest point? (c) How long does the ball take to hit the ground after it reaches its highest point? (d) What is its velocity when it returns to the level from which it started? 2. It is possible to shoot an arrow at a speed as high as 100 m/s. (a) If...
. ioins the Equation of motion, displacement Y is the function of time, time t is...
. ioins the Equation of motion, displacement Y is the function of time, time t is variable, for a given time t, there is A function value Y is corresponding to. Velocity V is first derivative of displacement Y, time is variable. for a given time t, there is a function value V is corresponding to. 5) Tabulating and plotting: (30 points), for a shouting up from a building problem, ye 49t2 1st.50, Y(t) 50 55.743? 44.2570 0 1.531? 0...
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find the first-order correction, y (t),...
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find the first-order correction, y (t), for the initial value problem with є * 0 and є is a small parameter.
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find...
Free-fall notion 1. A ball is thrown vertically upward at an initial speed of 49 m/s....
Free-fall notion 1. A ball is thrown vertically upward at an initial speed of 49 m/s. Assume that the ball leaves the hand when it is 15 m above the ground (about the height of Kirkbride), and that the effects of air resistance can be ignored. Choose your landmark to be the ground; then at t -0, yo- +15 m, Vyo +49 m/s a. 5 pts) How fast is the launch speed in mph? Do you think this is a...
Consider the initial value problem dy 3 2- y = 3t + 2e', y(0) = yo...
Consider the initial value problem dy 3 2- y = 3t + 2e', y(0) = yo . and for yo > Ye, (a) Find the critical value of yo, yc, such that for yo < yc, limt 400 y(t) = - limt700 y(t) = 0. (b) What happens if yo = ye?
(1 point) Consider the initial value problem y"36y g(t), y(0) 0, /(0) 0, t if 0<t<5 0 if 5t<00. where g(t)...
(1 point) Consider the initial value problem y"36y g(t), y(0) 0, /(0) 0, t if 0<t<5 0 if 5t<00. where g(t) create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from a. Take the Laplace transform of both sides the given differential equation one side of the equation the other (until you get to part (b) below). help (formulas) b. Solve your equation for Y(s). Y(s) C{y(t)} solve for y(t) c....
Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0)...
Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0) = 0, where where | 1 if t < 1, g(t) = { 10 if t > 1 (t) = { for all t. Is this solution unique for all time? Is it unique for any time? Does this contradict the existence and uniqueness theorem? Explain. (b) If the initial condition y(0) = 0 were replaced with y(1) = 0, would there necessarily be...
(1 point) Consider the initial value problem y' + 3y = 0 if 0 <t <3...
(1 point) Consider the initial value problem y' + 3y = 0 if 0 <t <3 9 if 3 < t < 5 0 if 5 <t< oo, y(0) = 3. (a) Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y by Y. Do not move any terms from one side of the equation to the other (until you get to part (b) below). y(s)(5+6)...
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) =...
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
Consider the differential equation: -9ty" – 6t(t – 3)y' + 6(t – 3)y=0, t> 0. a....
Consider the differential equation: -9ty" – 6t(t – 3)y' + 6(t – 3)y=0, t> 0. a. Given that yı(t) = 3t is a solution, apply the reduction of order method to find another solution y2 for which yı and y2 form a fundamental solution set. i. Starting with yi, solve for w in yıw' + (2y + p(t)yı)w = 0 so that w(1) = -3. w(t) = ii. Now solve for u where u = w so that u(1) =...
1. A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise? (b) How long does it take to reach its highest point? (c) How long does the ball take to hit the ground after it reaches its highest point? (d) What is its velocity when it returns to the level from which it started? 2. It is possible to shoot an arrow at a speed as high as 100 m/s. (a) If...
. ioins the Equation of motion, displacement Y is the function of time, time t is variable, for a given time t, there is A function value Y is corresponding to. Velocity V is first derivative of displacement Y, time is variable. for a given time t, there is a function value V is corresponding to. 5) Tabulating and plotting: (30 points), for a shouting up from a building problem, ye 49t2 1st.50, Y(t) 50 55.743? 44.2570 0 1.531? 0...
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find the first-order correction, y (t), for the initial value problem with є * 0 and є is a small parameter.
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find...
Free-fall notion 1. A ball is thrown vertically upward at an initial speed of 49 m/s. Assume that the ball leaves the hand when it is 15 m above the ground (about the height of Kirkbride), and that the effects of air resistance can be ignored. Choose your landmark to be the ground; then at t -0, yo- +15 m, Vyo +49 m/s a. 5 pts) How fast is the launch speed in mph? Do you think this is a...
Consider the initial value problem dy 3 2- y = 3t + 2e', y(0) = yo . and for yo > Ye, (a) Find the critical value of yo, yc, such that for yo < yc, limt 400 y(t) = - limt700 y(t) = 0. (b) What happens if yo = ye?
(1 point) Consider the initial value problem y"36y g(t), y(0) 0, /(0) 0, t if 0<t<5 0 if 5t<00. where g(t) create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from a. Take the Laplace transform of both sides the given differential equation one side of the equation the other (until you get to part (b) below). help (formulas) b. Solve your equation for Y(s). Y(s) C{y(t)} solve for y(t) c....
Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0) = 0, where where | 1 if t < 1, g(t) = { 10 if t > 1 (t) = { for all t. Is this solution unique for all time? Is it unique for any time? Does this contradict the existence and uniqueness theorem? Explain. (b) If the initial condition y(0) = 0 were replaced with y(1) = 0, would there necessarily be...
(1 point) Consider the initial value problem y' + 3y = 0 if 0 <t <3 9 if 3 < t < 5 0 if 5 <t< oo, y(0) = 3. (a) Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y by Y. Do not move any terms from one side of the equation to the other (until you get to part (b) below). y(s)(5+6)...
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
Consider the differential equation: -9ty" – 6t(t – 3)y' + 6(t – 3)y=0, t> 0. a. Given that yı(t) = 3t is a solution, apply the reduction of order method to find another solution y2 for which yı and y2 form a fundamental solution set. i. Starting with yi, solve for w in yıw' + (2y + p(t)yı)w = 0 so that w(1) = -3. w(t) = ii. Now solve for u where u = w so that u(1) =...
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