Question

How can I convert a second orde ODE into a first-order coupled equation in terms of the variables of X and P for a simple harmonic oscillator using the Hamiltonian Equation?

Answer #1

What is the difference between zero, first, and second order
chemical reactions in terms of the form of their rate equation and
how can I graph concentration-time data showing which order they
are?

Q.3 (Applications of Linear Second Order ODE): Consider the
‘equation of motion’ given by ODE d2x + ω2x = F0 cos(γt)
dt2
where F0 and ω ̸= γ are constants. Without worrying about those
constants, answer the questions (a)–(b).
(a) Show that the general solution of the given ODE is [2 pts]
x(t) := xc + xp = c1 cos(ωt) + c2 sin(ωt) + (F0 / ω2 − γ2)
cos(γt).
(b) Find the values of c1 and c2 if the...

In lab you create a system where the Hamiltonian can be written
as ? = ?0 + ?,
where ?0 is the Simple Harmonic Oscillator
Hamiltonian,,-h22md2dx2+12kx2
, and ? is an applied
perturbation given by, Dx4.
What is the first order correction to the energy ground state
energy,
Ψ0=mωℏπ14
e(-mωx22ℏ)
What is the first order correction to the first excited state
energy,
Ψ1=mωℏπ142mωℏ
xe-mωx22ℏ
For the Simple Harmonic Oscillator system, the fundamental
frequency is the v=0 to v=1
transition. Based...

solve the second order ode ( I have problem to choose right yp
for term has cosh or sinh)
y"-6y'+y=6 cosh x
y(0)=0.2
y'(0)=0.05

Consider the second order differential equation d2/dt^2 x + 6
dx/dt + 10x = 0. Classify the harmonic oscillator
(undamped, underdamped, critically damped, over damped). Justify
your answer.

Imagine a harmonic oscillator with Hamiltonian H=p^2/2m+½x^2 For
simplicity, we will assume that m=ℏ=1. First, we set up our system
in the first excited state of this Hamiltonian. Second, we turn on
an extra potential, V_ex(x)=x^4. Third, before the added potential
has a chance to change the system state, we measure the energy.By
expressing H and V_ex in terms of the raising and lowering
operators, evaluate the average energy we would see if we repeated
this whole process many times.

Consider the Bernoulli equation ?′ + (1/x)? = ?33 a.
Convert to a first order linear equation in ? in standard
form.
b. Write the integrating factor ? and solve for ?.

I have a simple question. Can a fourth order polynomial equation
be solved by hand? Or do you need to use computer program or
calculator program to solve it? For example you can solve second
order polynomial equation using quadratic equation if you want to
solve it by hand. Can you do something similar with fourth order?
Or does it have to be done on math programs?

10.16: Write a user-defined MATLAB function that solves a
first-order ODE by applying the midpoint method (use the form of
second-order Runge-Kutta method, Eqs(10.65),(10.66)). For function
name and arguments use [x,y]=odeMIDPOINT(ODE,a,b,h,yINI). The input
argument ODE is a name for the function that calculates dy/dx. It
is a dummy name for the function that is imported into odeMIDPOINT.
The arguments a and b define the domain of the solution, h is step
size; yINI is initial value. The output arguments, x...

How
do we know which order of differencial equation we would use to
find 1st ODE
e.g
Seperable
linear
homogeneous
exact/non exact
bernoulli
which one do we consider first..? To determine which
differcial equation we will use?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 7 minutes ago

asked 16 minutes ago

asked 28 minutes ago

asked 35 minutes ago

asked 36 minutes ago

asked 42 minutes ago

asked 43 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago