Boundary Value Problem based on specific problem
2 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
clear all;
close all;
clc;
%% INPUTs:
f = 6; % Natural Cyclic Frequency (1/sec or Hertz-Hz)
x0 = 0.02; % Initial Displacement (in m)
v0 = 0.25; % Initial Velocity (in m/s)
%% OUTPUTs:
wn = 2*pi()*f % Natural Circular Frequency or Angular Frequency (rad/s)
T = 1/f % Fundamental Time-Period (sec)
A = sqrt((x0^2) + (v0/wn)^2) % Amplitude (m)
vm = A*wn % Maximum Velocity (m/s)
am = vm*wn % Maximum Acceleration (m/s/s)
Phi = atand(x0*wn/v0) % Phase Angle (in degree)
syms X(t)
E = diff(X,t,2) + (wn^2)*X == 0;
x = dsolve(E) % C1 & C2 are constant and can be determined by BCs
%% I need to find constant C1 & C2 through boundary value problem as x(0) = 0 & x'(0)=0. Can someone help me out?
0 Kommentare
Akzeptierte Antwort
Torsten
am 28 Feb. 2024
Verschoben: Torsten
am 28 Feb. 2024
x(0) = 0 gives C1 = 0, x'(0) = 0 gives C2 = 0. Thus the solution of your equation is x = 0 for all t.
2 Kommentare
Torsten
am 29 Feb. 2024
clear all;
close all;
clc;
%% INPUTs:
f = 6; % Natural Cyclic Frequency (1/sec or Hertz-Hz)
x0 = 0.02; % Initial Displacement (in m)
v0 = 0.25; % Initial Velocity (in m/s)
%% OUTPUTs:
wn = 2*pi()*f % Natural Circular Frequency or Angular Frequency (rad/s)
T = 1/f % Fundamental Time-Period (sec)
A = sqrt((x0^2) + (v0/wn)^2) % Amplitude (m)
vm = A*wn % Maximum Velocity (m/s)
am = vm*wn % Maximum Acceleration (m/s/s)
Phi = atand(x0*wn/v0) % Phase Angle (in degree)
syms X(t)
E = diff(X,t,2) + (wn^2)*X == 0;
dX = diff(X,t);
conds =[X(0)==0.02,dX(0)==0.25];
x = dsolve(E,conds) % C1 & C2 are constant and can be determined by BCs
fplot(x,[0 1])
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Numerical Integration and Differential Equations finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!