Consider the following system (see attachment) whose state space representation is as follows:
a) Find the transfer function of the system.
b) Compute eAt using the eigenvalues and eigenvectors method.
c) Compute eAt using the partial fraction method.
d) If u (t)=0 for t ≥ 0,compute x (t), y(t), and x(1) =[ -1 2]T
e) Assume that the initial conditions are zero. Using MATLAB ,Plot x(t), y(t), given that u(t)= -5 for 0 ≤ t ≤ 3 and u(t)=5 for 3 ≤ t ≤ 6
Consider the following system whose state space representation is as follows:
x'1(t) 5 2 x1(t) 1
= + u(t)
x'2(t) -2 5 x2(t) 1
y(t) = [ 1 5 ] ...
The expert finds the transfer function from the state space representation.
Problems and Solutions to Statistical Mechanics Problems
List of solved problems:
Derive Strirling's approximation for N!.
Derive the Gaussian approximation of the binomial distribution.
Derive expressions for the mean and standard deviation for the binomial distribution.
Compute the pressure of an ideal Bose gas at absolute zero.
Compute the entropy of an ideal gas using the micro-canonical ensemble.
Compute the internal energy of N harmonic oscillators as a function of temperature using the micro-canonical ensemble.
Compute the susceptibility of a spin 1/2 particle .
Compute the entropy of a harmonic oscillator.
Compute the energy fluctuations of a system at constant temperature.
Compute the internal energy of a diatomic molecule.
Estimate the maximum possible height of trees.
Compute the temperature of the relic neutrino background of the universe.View Full Posting Details