Question

Determine whether cos ( k x ) e x p ( − i ω t ) is an acceptable solution to the time-dependent Schrödinger wave equation.

Answer #1

Show that E(x,t) = Emax. Cos (kx – wt)
And B(x,t) = Bmax. Cos (kx – wt)
Are solutions to the Wave Equations

Determine whether each of the following functions is a solution
of wave equation: a) u(x, t) = sin (x − at), b) u(x, t) = sin (x −
at) + ln (x + at)

A standing wave’s function is y(x,t) = Asin(kx)cos(?t). Prove
that this equation is indeed a solution to the wave equation.

Two waves, y1(x,t) and
y2(x,t), travel on the same piece of
rope and combine to produce a resultant wave of the form
y(x,t) = 8.000 sin(4.000x +
1.000t + 0)cos(1.000x + 3.000t + 0). The
first wave is y1(x, t ) = 4.000
sin(3.000x + (-2.000)t), while the second wave
has the form y2(x, t ) = A
sin(kx ± ωt+ϕ), where x is
measured in m and t in seconds. Determine the values of
the constants in the second...

A wave on a string is described by the equation
y(x, t) = 2*cos(2 π(x/4m- t /.1 s))
where x is in meters and t is in seconds.
a. Is the wave travelling to the right or to the left?
_________
b. What is the wave frequency? __________
c. What is the wavelength? ___________
d. What is the wave speed? _________
e. At t=0.50 seconds what is the displacement of the string at
x=0.20 meters. _________

Differential equations
Given that x1(t) = cos t is a solution of (sin t)x′′ − 2(cos
t)x′ − (sin t)x = 0, find a second linearly independent solution of
this equation.

Calculate Using Maltab.
The displacement of the oscillating spring can be described
by:
x = A*cos(ω*t)
where:
x = displacement at time t, +ve means upward -ve means
downwards
A = maximum displacement,
ω = angular frequency in radians per second, and
t = time in seconds
If the maximum displacement A = 4 cm and the angular frequency
is 0.6 radians per second.
What is the shortest time at which the displacement is equal to 2
cm (upwards)?
a)1.745...

(a)
Find the value of ω for which we can observe resonance
in the solution of the following IVP
19x″ + 25 x =
cos(ωt)
(b)
The equation of motion for x(t) is given by
the following equation
d 2x
dt2
+ 34
dx
dt
+ 289x = 0
Determine whether the system is overdamped, critically damped, or
underdamped.

A wave on a string is described by the equation y(x,t)=3.0
cm*〖cos(〗〖2π*(x/2.4m+t/(0.2 s)))〗 . X is in meters and t is in
seconds.
Is the wave travelling to the right or to the left?
_________
What is the wave speed? _________
What is the wave frequency? __________
What is the wavelength? ___________
At t=0.50 seconds what is the displacement of the string at
x=0.20 meters. _________

The position of an object at time t is given by: r(t)=e^−t i +
e^t j − t√2 k, 0≤ t<∞. (a) Determine the velocity v and the
speed of the object at time t. (b) Determine the acceleration of
the object at time t. (c) Find the distance that the object travels
during the time interval 0≤ t<ln3. Answers: (a) = velocity: v
=−e^−t i + e^t j − √2 k; speed: ||v||= e^t + e^−t, (b) =
acceleration:...

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