Discrepancy Between ODE45 and Solve

Im trying to solve a simple forced harmonic oscillators for different forcing frequencies. Solving it with Dsolve and plotting the solution returns the expected values that i found through hand calculations. Using matlab ODE 45 returns the exact same values as Dsolve but they are 10 times larger (10^-3 instead of 10^-4). I cant not figure out why there is a large discrepancy betweent the two methods. Any ideas?

Dsolve

syms x(t) w
 
xd = diff(x, t);
xdd = diff(xd, t);
 k = 4000; m = 10; c = 200;
wn = sqrt(k/m);
 
ode = sin(t*w) == xdd*m + k*x +c*xd;
cond = [x(0) == 0 , xd(0) == 0];
solu = dsolve(ode, cond);
equ = simplify(solu); 
 
    t = 0:.001:5;
 
for w = 10:4:30
    hold on
    data = eval(equ);
    plot(t, data,'DisplayName',num2str(w))
    xlabel('Time')
    ylabel('Displacement')
end 
legend

ODE

function dxdt=ex1(t,x,w)
wn= 20;
z= .5;
dxdt=[x(2);1*sin(w*t)-2*z*wn*x(2)-(wn^2)*x(1)];
%% 

%******ode45****Example*****************
clc; clear;
% w = 14.14;

for w = 10:4:30
    options = odeset('RelTol', 1e-13, 'AbsTol', 1e-15);
    [t,x]=ode45(@(t,x) HW361_7_1ODE(t,x,w), [0:.001:5] ,[0 0]);
% % % %     ***************************************
    
    hold on
%     subplot(3,1,1)
    plot(t,x(:,1),'DisplayName',num2str(w))
    grid
    xlabel('Time')
    ylabel('Displacement')
    legend
% % 
%     hold on
%     subplot(3,1,2)
%     plot(t,x(:,2),'DisplayName',num2str(w))
%     grid
%     xlabel('Time')
%     ylabel('Velocity') 
%     legend
%     
%     hold on
%     subplot(3,1,3)
%     plot(x(:,1), x(:,2),'DisplayName',num2str(w))
%     grid
%     xlabel('Displacement')
%     ylabel('Velocity')
%     legend
end

% %*********************************

[Torsten]

You forgot to divide sin(w*t) by a factor of 10 in the ode45 version.

Answer 1

[James Tursa]

For dslove, the sin(w*t) signal gets divided by m, which is 10.

For ode45, you don't do this, you just have sin(w*t).

[Andrew Bentz]

thatnk you very much,

I've been looking too much at the code and not enough at the math