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Solving Diff. Equations with Varied Conditions & Inputs - Prof. Pramod P. Khargonekar, Study notes of Electrical and Electronics Engineering

University of Florida (UF)Electrical and Electronics Engineering
Prof. Pramod P. Khargonekar

The fall 2011 homework 8 for eel 3105, which involves solving differential equations using various initial conditions and input functions. Students are required to find the solutions for y(t) when the differential equations have different initial conditions and input functions, including the unit step function, unit impulse function, and sinusoidal functions. Problem 2 asks students to apply the laplace transform method to solve the given differential equation.

Typology: Study notes

2010/2011

Uploaded on 12/30/2011

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EEL๎˜ƒ3105๎˜ƒFall๎˜ƒ2011๎˜ƒ
Homework๎˜ƒ8๎˜ƒ
๎˜ƒ๎˜ƒ
1. Solve๎˜ƒthe๎˜ƒfollowing๎˜ƒproblems๎˜ƒfor๎˜ƒboth๎˜ƒof๎˜ƒthese๎˜ƒthe๎˜ƒdifferential๎˜ƒequations๎˜ƒ
๎˜ƒ
2
2
2
2
616()
12 16 ( )
dy dy yut
dt dt
dy dy yut
dt dt
๏€ซ๏€ซ๏€ฝ
๏€ซ๏€ซ๏€ฝ
๎˜ƒ
A. Suppose๎˜ƒy(0)=0,๎˜ƒ(0) 0
dy
dt ๏€ฝ๎˜ƒand๎˜ƒu=U(t)๎˜ƒwhere๎˜ƒU(t)๎˜ƒis๎˜ƒthe๎˜ƒunit๎˜ƒstep๎˜ƒfunction.๎˜ƒFind๎˜ƒy(t).๎˜ƒ
B. Suppose๎˜ƒy(0)๎˜ƒ=1,
๎˜ƒ
(0) 0
dy
dt ๏€ฝ๎˜ƒand๎˜ƒu=unit๎˜ƒimpulse๎˜ƒfunction.๎˜ƒFind๎˜ƒy(t).๎˜ƒ
C. Suppose๎˜ƒy(0)=0,๎˜ƒ(0) 0
dy
dt ๏€ฝand๎˜ƒu(t)=5sin(20๏ฐt).๎˜ƒFind๎˜ƒy(t).๎˜ƒ
D. Suppose๎˜ƒy(0)=1,๎˜ƒ(0) 0
dy
dt ๏€ฝand๎˜ƒu(t)=5sin(20๏ฐt).๎˜ƒFind๎˜ƒy(t).๎˜ƒ
E. Suppose๎˜ƒy(0)=1,๎˜ƒ(0) 0
dy
dt ๏€ฝand๎˜ƒu(t)=5U(t)๎˜ƒwhere๎˜ƒU(t)๎˜ƒis๎˜ƒthe๎˜ƒunit๎˜ƒstep๎˜ƒfunction.๎˜ƒFind๎˜ƒy(t).๎˜ƒ
2. Solve๎˜ƒProblem๎˜ƒ1๎˜ƒusing๎˜ƒthe๎˜ƒLaplace๎˜ƒtransform๎˜ƒmethod.๎˜ƒ
๎˜ƒ

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Download Solving Diff. Equations with Varied Conditions & Inputs - Prof. Pramod P. Khargonekar and more Study notes Electrical and Electronics Engineering in PDF only on Docsity!

EEL 3105 Fall 2011

Homework 8

  1. Solve the following problems for both of these the differential equations

2 2 2 2

d y dy (^) y u t dt dt d y dy (^) y u t dt dt

A. Suppose y(0)=0,^ dy (0) 0 dt

๏€ฝ and u=U(t) where U(t) is the unit step function. Find y(t).

B. Suppose y(0) =1,^ dy (0) 0 dt

๏€ฝ and u=unit impulse function. Find y(t).

C. Suppose y(0)=0,^ dy (0) 0 dt

๏€ฝ and u(t)=5sin(20๏ฐt). Find y(t).

D. Suppose y(0)=1,^ dy (0) 0 dt

๏€ฝ and u(t)=5sin(20๏ฐt). Find y(t).

E. Suppose y(0)=1,^ dy (0) 0 dt

๏€ฝ and u(t)=5U(t) where U(t) is the unit step function. Find y(t).

  1. Solve Problem 1 using the Laplace transform method.