Question
In: Advanced Math
Consider the force, but undamped system described by the initial value problem u'' + u =...
Consider the force, but undamped system described by the initial value problem u'' + u = 3 cos(ωt), u(0) = 0, u'(0) = 0 (a) Find the solution u(t) for ω != 1. (b) Find the solution u(t) for ω = 1 (Resonance)
Solutions
Colby Messinger answered 2 years agoRelated Solutions
Consider a vibrating system described by the initial value problem. (A computer algebra system is recommended.)...
Consider a vibrating system described by the initial value
problem. (A computer algebra system is recommended.) u'' + 1/4u' +
2u = 2 cos ωt, u(0) = 0, u'(0) = 6
(a) Determine the steady state part of the solution of this
problem.
u(t) =
(b) Find the amplitude A of the steady state solution in
terms of ω.
A =
(d) Find the maximum value of A and the frequency ω for
which it occurs.
Consider an initial value problem ?′′ + 2? = ?(?) = cos? (0 ≤ ? <...
Consider an initial value
problem
?′′ + 2? = ?(?) = cos? (0 ≤ ? < ?) , 0 (? ≥
?)
?(0) = 0 and ?′(0) = 0
(a) Express ?(?) in terms of the unit step function.
(b) Find the Laplace transform of ?(?).
(c) Find ?(?) by using the Laplace transform method.
Consider the following initial value problem: ?? − 2?? = √? − 2? + 3 ??...
Consider the following initial value problem: ?? − 2?? = √? − 2?
+ 3 ?? ?(0) = 6
1. Write the equation in the form ?? ?? = ?(?? + ?? + ? ), where
?, ?, ??? ? are constants and ? is a function.
2. Use the substitution ? = ?? + ?? + ? to transfer the equation
into the variables ? and ? only.
3. Solve the equation in (2).
4. Re-substitute ? = ??...
Problem 1: Consider the following Initial Value Problem (IVP) where ? is the dependent variable and...
Problem 1: Consider the following Initial Value Problem (IVP)
where ? is the dependent variable and ? is the independent
variable: ?′=sin(?)∗(1−?) with ?(0)=?0 and ?≥0
Note: the analytic solution for this IVP is:
?(?)=1+(?_0−1)?^cos(?)−1
Part 1A: Approximate the solution to the IVP using Euler’s method
with the following conditions: Initial condition ?_0=−1/2; time
step ℎ=1/16; and time interval ?∈[0,20]
+ Derive the recursive formula for Euler’s method applied to this
IVP
+ Plot the Euler’s method approximation
+ Plot...
Problem 1: Consider the following Initial Value Problem (IVP) where ? is the dependent variable and...
Problem 1: Consider the following Initial Value Problem (IVP)
where ? is the dependent variable and ? is the independent
variable: ?′=sin(?)∗(1−?) with ?(0)=?0 and ? ≥ 0
Note: the analytic solution for this IVP is: y(t) =
1+(y_0 - 0)e^
cos(t)-1
Part 1B: Approximate the solution to the IVP using the Improved
Euler’s method with the following conditions: Initial condition
?0=−1/2; time step ℎ=1/16; and time interval ?∈[0,20]
+ Derive the recursive formula for the Improved Euler’s method
applied...
Problem 1: Consider the following Initial Value Problem (IVP) where ? is the dependent variable and...
Problem 1: Consider the following Initial Value Problem (IVP)
where ? is the dependent variable and ? is the independent
variable: ?′=sin(?)∗(1−?) with ?(0)=?0 and ?≥0
Note: the analytic solution for this IVP is:
?(?)=1+(?_0−1)?^cos(?)−1
Part 1A: Approximate the solution to the IVP using Euler’s method
with the following conditions: Initial condition ?_0=−1/2; time
step ℎ=1/16; and time interval ?∈[0,20]
+ Derive the recursive formula for Euler’s method applied to this
IVP
+ Plot the Euler’s method approximation
+ Plot...
Solve the following initial value problem ut + 2ux − 2u = e t+2x , u(x,...
Solve the following initial value problem ut + 2ux − 2u = e t+2x
, u(x, 0) = 0
Consider the following initial value problem to be solved by undetermined coefficients. y″ − 16y =...
Consider the following initial value problem to be solved by
undetermined coefficients. y″ − 16y = 6, y(0) = 1, y′(0) = 0
Write the given differential equation in the form L(y) = g(x)
where L is a linear operator with constant coefficients. If
possible, factor L. (Use D for the differential operator.)
( )y = 16
Consider this initial-rate data at a certain temperature for the reaction described by :  
Consider this initial-rate data at a certain temperature for the
reaction described by
:
OH-(aq)
OCl-(aq) + I- (aq) --------------> OI-(aq) + Cl-(aq)
Trial [OCl-]0
(M)
[I-]0
(M)
[OH-]0
(M)
Initial rated (M/s)
1
0.00161
0.00161
0.530
0.000335
2
0.00161
0.00301
0.530
0.000626
3
0.00279 0.00161
0.710
0.000433
4
0.00161
0.00301
0.880
0.000377
Determine the tate law and the value of the rate constant for
this reaction.
Consider the initial value problem y′ = 18x − 3y, y(0) = 2 (a) Solve it...
Consider the initial value problem
y′ = 18x − 3y, y(0) = 2
(a) Solve it as a linear 1st order ODE with the method of the
integrating factor.
(b) Solve it using a substitution method.
(c) Solve it using the Laplace transform.
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