Consider the following initial value problemso0

Given initial value problem is y''(t)-5y(t)=g(t)whereg(t)=00≤t<4et-44≤t<∞Initial conditions…

Answered: Consider the following initial value…

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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If g(t) = −3t¹ – 5t² – 6 find g(0) g'(0) g" (0) g"" (0) g(4) (0) g(5) (0)
= A mass m = 4 kg is attached to both a spring with spring constant k 577 N/m and a dash-pot with damping constant c = 4 N. s/m. The mass is started in motion with initial position o 3 m and initial velocity = 5 m/s. Determine the position function z(t) in meters. x(t) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form r(t) Ciecos (wit-a₁). Determine C₁, w₁,ajand p. C₁ WI XX1 P = 11 Co (e^(-1/2t))[((-5/6)sin(12t))+(3cos(12t))] Graph the function z(t) together with the "amplitude envelope" curves z-C₁e- and = ₁e pt. Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected ( so c= 0). Solve the resulting differential equation to find the position function u(t). In this case the position function u(t) can be written as u(t)= Cocos (wotao). Determine Co. we and co. = ولما (assume 0 ≤ a <2m)
10. The half-life of krypton-91 (" Kr) is 10 seconds. At time t = 0, a heavy canister contains 3 grams of this radioactive gas. a. Find a function A(t)= P,M that models the amount of " Krremaining in the canister after t seconds. b. Find a function A(t)= Pe" that models the amount of Krremaining in the canister after t seconds. c. How much " Kr remains after 2 minutes? d. After how long will the amount of "Kr remaining be reduced to 1 ug (microgram or 10* grams?
Find a > 1 to express y = 3(2/9)x in the form y = 3(a−x)
2. Consider the three functions below: S(x) = 2r S(z) =r S(z) = 2 (a) Create a t-table for cach of the three functions, using the x-values-2, -1, 0, 1, 2, and 3. (b) Which function appears to be growing the fastest? That is, for which function are the y-values increasing the fastest? (c) On the same set of axes, graph all three of the functions above. Be sure to scale your axes! Was your answer to part b correct?
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2
2. Water tides can be modelled using the function_h(t)=6.6sin[(t+3)]+7.8 where h(t) is the height of water at time t (in hours) after midnight. The height of the water at high tide is a m and the height of the water at low tide is d m. On a particular day, the first high tide occurs at midnight. (a) Using the information given to find the values of a and d. (b) Determine the length of time between two high tides.
a. Determine if the particle is speeding up or slowing down at time t=0 b. If the particle is initially located 1cm to the left of the origin, find the position function of the particle at any time t. please write clearly and compelte solution and i will upvote

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Consider the following initial value problem 0