Dynamic Analysis of a Second-Order System with Harmonic Loading
Dynamic Analysis of a Second-Order System with Harmonic Loading
This Demonstration gives a complete analysis of a second-order system with harmonic loading. The system's differential equation is , where , is the mass of the system, is the damping coefficient, is the stiffness, is the magnitude of the force, and is the force frequency. The response is plotted as a function of time for the underdamped, critically damped, and overdamped cases. This Demonstration displays the transient response (the homogeneous part of the total solution), the steady state response (the particular part of the total solution), and the total response, which is the combination of the two. You can see the analytical solution for each case by moving the mouse over the response curve. Separate displays are given for the dynamic magnification factor and the phase of the response relative to the force. A number of pre-configured test cases can be chosen, to illustrate several important cases of system responses under different loading conditions.
mu″+cu′+ku=f(t)
f(t)=Fsin(ϖt)
m
c
k
F
ϖ
u(t)