Problem 1: Consider a time-varying population that follows the logistic population model. The population has a limiting population of 800, and at time t = 0, its population of 200 is growing at a rate of 60 per year. a) Write a differential equation for the population Solution: Put your math/explanation here... P(t). that models this scenario. b) Identify an appropriate solution technique and solve this differential equation. Solution: Put your math/explanation here... c) Use MATLAB to plot your solution for 1 = 0 to 1 = 10. Solution: code Home -0% Normal text X 1 pogle.com/document/d/1kZySZ9ztaBeg3FOckXKD 8BNPzefWpliqcB89GCwDmg/edit ct One MATLAB Template nsert Format Tools Extensions Help MyMathLab Homework x Arial Solution: Last edit was seconds ago G + BIU A Solution: Put your math/explanation here... Do Homework-4-1 Myi x 1 d) How long will it take for the population to achieve 95% of its maximum population? Pg 2 26265 My Drive-Google Drive x 1 e) Use the MATLAB dsolve() function to solve the differential equation and plot the solution on a new figure. The results provided by dsolve() and your solution from part (b) should match. FE @ Q- =- ==-- TA MAT 3: Home gle.com/drive/my-drive | 1 MyMathLab Homework x V(t) R www Do Homework-4-1 My x Problem 2: Consider the RLC circuit shown below, where the inital current flowing through the circuit at time t = 0 is Io = 5, and the initial charge on the capacitor at time t = 0 is 20 = 2. C Pg 3 L 3 My Drive - Google Drive x I month G com MAT 330 Project One M x a) Write a differential equation for Q(1), the charge across the capacitor, assuming the voltage source V(1) = 0. Solution: + Home om/drive/my-drive X b) Classify the differential equation Solution: Put your math/explanation here... MyMathLab Homework X Solution: Put your math/explanation here... code d) Use MATLAB to plot your solution for time t = 0 to 1. Solution: Solution: Scode Do Homework-4-1 My X c) Identify an appropriate solution technique, and solve the differential equation for Q(t). Pg 4 My Drive- Google Drive x 2 d I w m e) Use the MATLAB dsolve() function to solve the differential equation and plot the solution on a new figure. The results provided by dsolve() and your solution from part (b) should match. MAT 330 Project One M x Home om/drive/my-drive X 1 MyMathLab Homework xDo Homework - 4-1 My x Unstretched Pg 5 12 Problem 3: Consider the spring-mass system shown below. A mass of m = 5 kg has stretched a spring by so = 1.5 meters and is at rest. A damping system is connected that provides a damping force equal to 30 times the instantaneous velocity of the mass. At time / = 0, the mass at rest has an external force of f(t) = 25 sin (10t) applied. k 3 My Drive- Google Drive x s I FEEST MAT 330 Projec he drive/my-drive x | - My MathLab Homework xDo Homework -4-1 My x LAB Template.pdf Unstretched y = 0 m k Pg 6 Open with m C H f(t) 4 / 5 Page a) Write a differential equation that models the mass location y(7)as a function of time. Solution: Put your math/explanation here.... asm My Drive - Google Drive x Q + THESE MAT 330 Project One Home gle.com/drive/my-drive My MathLab Homework x Do Homework-4-1 My x Solution: Put your math/explanation here... b) Identify an appropriate solution technique, and solve the differential equation for y(1). c) Use MATLAB to plot your solution for t = 0 to 1 = 20. Solution: code d) What is the steady-state solution of y(1)? Solution: Put your math/explanation here.... MABELLA My Drive - Google Drive x Pg 7 SERIE www I e) Use the MATLAB dsolve() function to solve the differential equation and plot the solution on a new figure. The results provided by dsolve() and your solution from part (b) should match. Solution: MAT 330 Project One