I am trying to find the displacement of this below 2nd order differential equation.

4 ビュー (過去 30 日間)
Lokesh Katari
Lokesh Katari 2021 年 8 月 19 日
コメント済み: Wan Ji 2021 年 8 月 19 日
where x is the displacement and g is the acceleration due to gravity.
how to solve this equation in matlab. can anyone please help as it is new to me.
Thanks

回答 (2 件)

Wan Ji
Wan Ji 2021 年 8 月 19 日
編集済み: Wan Ji 2021 年 8 月 19 日
Hi, friend! The ode you provided is a 2nd order ode. Follow the code you will know how to solve this ode. But at first, since both the mass m and the stiffness K is positive, the equation should be modified as:
Then the code is
% Firstly, define the ode function
% Here we set x(1)=x and x(2)=x';
% Then odefun = [x'; x''] = [x(2); -K/m*x*(1)+g]
odefun = @(t,x, K, m, g)[x(2); -K/m*x(1)+g];
K = 1; % set stiffness
m = 1; % set mass
g = 10; % set gravity
x0 = [0;0]; % set the initial conditions [initial position and initial velocity]
tspan = 0:0.1:20; % set t span
[t, x] = ode45(@(t,x)odefun(t, x, K, m, g), tspan, x0); % solve with ode45
plot(t,x(:,1),'r-') % plot results
hold on
plot(t,x(:,2),'b-')
xlabel('t'); ylabel('x or dx/dt')
legend('x','dx/dt')
  1 件のコメント
Wan Ji
Wan Ji 2021 年 8 月 19 日
Since this ode can also be solved by dsolve (Notice that only a few odes can be solved analytically), here I post how to use this symbolic tool.
First we define
and set ω a positive real number.
The initial condition: the initial position x and initial velocity are denoted by x01 and x02 respectively in this demo.
syms x(t) x01 x02 g
syms omega real positive
eq = diff(x,2) + omega^2*x - g ==0; % pde
Dx = diff(x,1); % x'
conds = [ x(0) == x01, Dx(0) == x02]; % initial conditions
x = dsolve(eq, conds)
The result is (calculated in the *mlx file )

サインインしてコメントする。


Krishna Sutar
Krishna Sutar 2021 年 8 月 19 日
Please refer to dsolve documentation where you understand how to solve differential equations in MATLAB. Few examples are also provided in the documentation.

製品


リリース

R2019b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by