A common solution to the wave equation is E(x,t) = A
e^i(kx+wt). On paper take the...
A common solution to the wave equation is E(x,t) = A
e^i(kx+wt). On paper take the needed derivatives and
show that it actually is a solution. Note that i is the square-root
of -1.
Consider the following one-dimensional partial differentiation
wave equation. Produce the solution u(x, t) of this equation. 4Uxx
= Utt 0 < x 0 Boundary Conditions: u (0, t) = u (2π, t) = 0,
Initial Conditions a shown below: consider g(x)= 0 in both
cases.
(a) u (x, 0) = f(x) = 3sin 2x +3 sin7x , 0 < x <2π
(b) u (x, 0) = x +2, 0 < x <2π
1. If
y(x,t) = (8.4 mm) sin[kx + (770 rad/s)t
+ φ]
describes a wave traveling along a string, how much time does any
given point on the string take to move between displacements
y = +1.2 mm and y = -1.2 mm?
2.A sinusoidal wave travels along a string. The time for a
particular point to move from maximum displacement to zero is 0.25
s. What are the (a) period and
(b) frequency? (c) The wavelength
is 2.0 m;...
(i) Write down the wave equation and find the general solution
for longitudinal vibration of a beam using the method of separation
of variable separation.
(ii) Find three lowest natural frequencies of longitudinal
vibration of 1.5m beam with free-free boundary conditions at the
ends. The modules of elasticity is 200e^9 N/m and density 7500
kg/m3.
X(t)=Atan(wt)+Bcot(wt) and Y(t)=Btan(wt)+Acot(wt) both are
random process, w is a constant, A and B are zero-mean and
variance of A and B is σ ^2, they are independent
random variables,
a-) find autocorrelation function of X(t) and Y(t)
b-) find the cross correlation function of X(t) and Y(t)
A mechanical wave is given by the equation: y(x,t) = 0.5 cos
(62.8x – 15.7t) , Find: (1) Amplitude, frequency, wavelength? (2)
The velocity of the wave? (3) The maximum velocity of the
vibrations? (4) Write down the equation in the opposite
direction?