Question

x''+x=cost

1-how do you find the transient solution?

2-Find the steady state solution?

How do you graph the phase portrait

Answer #1

Describe both the transient and the steady-state solution of
the forced
spring-mass system: x'' + 2x' + 3x = sin(t).

a) Find the steady-state vector for the transition matrix.
.8
1
.2
0
x= ______
__________
b) Find the steady-state vector for the transition matrix.
1
7
4
7
6
7
3
7
These are fractions^
x= _____
________

Solve the heat equation and find the steady state solution:
uxx = ut, 0 < x < 1, t > 0,
u(0,t) = T1, u(1,t) = T2, where T1
and T2 are distinct
constants, and u(x,0) = 0

The solution to the Initial value problem
x′′+2x′+2x=2cos(7t),x(0)=0,x′(0)=0 is the sum of the steady
periodic solution xsp and the transient solution xtr. Find both xsp
and xtr.
xsp=
xtr=

The solution to the Initial value problem
?″+2?′+82?=4cos(9?),?(0)=0,?′(0)=0
is the sum of the steady periodic solution ???xsp and the
transient solution ???xtr. Find both ???xsp and ???xtr.

Solve the heat equation and find the steady state solution :
uxx=ut 0<x<1, t>0,
u(0,t)=T1, u(1,t)=T2, where T1 and T2 are
distinct constants, and u(x,0)=0

following nonlinear system:
x' = 2 sin y,
y'= x^2 + 2y − 1
find all singular points in the domain x, y ∈ [−1, 1],determine
their types and stability.
Find slopes of saddle separatrices.
Use this to sketch the phase portrait in the domain x, y ∈ [−1,
1].

In each of Problems 1 through 8, find the steady-state solution
of the heat conduction equation α2uxx = ut that satisfies the given
set of boundary conditions.
1. ux (0, t) = 0, u( L, t) = 0
2. u(0, t) = 0, ux ( L, t) = 0

Intermediate Macroeconomics
1. Use the steady state capital graph to show how an
decrease in savings rate affects the steady state capital stock per
person and steady state output per person.

Consider a damped forced mass-spring system with m = 1, γ = 2,
and k = 26, under the influence of an external force F(t) = 82
cos(4t).
a) (8 points) Find the position u(t) of the mass at any time t,
if u(0) = 6 and u 0 (0) = 0.
b) (4 points) Find the transient solution uc(t) and the steady
state solution U(t). How would you characterize these two solutions
in terms of their behavior in time?...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 20 minutes ago

asked 22 minutes ago

asked 22 minutes ago

asked 29 minutes ago

asked 29 minutes ago

asked 30 minutes ago

asked 47 minutes ago

asked 49 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago