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

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...

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?

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.

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 ?.

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?

The radioisotope studies today decays following either zero
order or first order, or second order kinetics. The graphs produced
by the integrated rate law plot different variables on the x and y
axis depending on the order of the reaction. Look up in your
textbook for the straight line plots of these three types of rate
laws. Draw the plots in your notebook and label it. Give an
equation that can be use to determine the half life of the...

When looking at a graph how do you know if it is zero order,
first order, second order. Would I be right to assume that if the y
axis, would be In HOF for first order, HOF for zero order, and
1/HOF for second order. Would the equation y = mx+b change. For
example y = -0.17x-0.61 change? What would be an example of the
equation for zero, first and second order?

3. a. For both (i) and (ii) below, use the first and second
order conditions to find (and verify) the profit maximizing level
of output and then find the level of profits associated with this
quantity. This is a price taking firm in a perfectly competitive
industry. b. For both (i) and (ii) below, find the minimum price at
which each firm is willing to produce a positive level of output.
Show all work. (i) P = $240, and C(q)...

How can I alter this Java method so that I convert and then
return every sentence in the array of strings instead of just the
first sentence?
public static char[] charConvert ( String [] sentences ) {
int totLength = sentences[0].length() + sentences[1].length() +
sentences[2].length() + sentences[3].length() +
sentences[4].length();
char [] letter = new char[totLength];
int x = 0;
int y = 0;
while ( y < sentences[x].length() ) {
switch ( sentences[x].charAt(y) ) {
case 'a': case 'A':...

How can you convert benzene to the following compounds using
this list of reagents?
1. HNO3, H2SO4 2.
SO3, H2SO4 3.
NaNO2, HCl 4. Br2,
FeBr3 5. Cl2,
FeCl3
6. CuCN 7. CuCl 8.
CuBr 9. H2O, ∆ 10.
CH3CH2CH2Cl, AlCl3
11. CH3CH2COCl (an acid chloride),
AlCl3 12. Zn-Hg, EtOH, HCl 13.
(1. Sn, HCl 2. NaOH, H2O)
14. CH3Cl ,
AlCl3 15.
KMnO4
A) m-nitropropylbenzene
B) p-nitropropylbenzene
I tried 1, 10 for the first one and 10, 1 for...

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