Question

In: Advanced Math

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.

Solutions

Expert Solution


Related Solutions

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)
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.
Use a computer algebra system to graph f and to find f ' and f ''....
Use a computer algebra system to graph f and to find f ' and f ''. Use graphs of these derivatives to find the following. (Enter your answers using interval notation. Round your answers to two decimal places.) f(x) = x3 + 5x2 + 1 x4 + x3 − x2 + 2 The intervals where the function is increasing. The intervals where the function is decreasing. The local maximum values of the function. (Enter your answers as a comma-separated list.)...
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...
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
Solve the initial value problem using systems of Linear Differential Equations. Please try to use computer...
Solve the initial value problem using systems of Linear Differential Equations. Please try to use computer typing x’ – 4y = 3 x + y’ = 2 IVP: x(0) = 0, y(0) = 1
Consider this initial-rate data at a certain temperature for the reaction described by :                           &nbsp
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.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT