Numerically integrating Acceleration to get displacement?

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KLETECH MOTORSPORTS
KLETECH MOTORSPORTS 2020-11-15
评论： Ameer Hamza 2020-11-15
I want to rephrase my last question, as i was not very clear there.
What i am trying to do is integrate the following second order, nonlinear ode, which is an expression for angular acceleration,
twice, to get the displacement, and compare it with the actual expression for displacement:
BOTH ω and A are specified initially. They are constants.
------------------------------------equation for acceleration
(corrected from )
if initial conditions are required, then x(0)=pi/4 and dx/dt (t=0) =0
this has to be integrated w.r.t time, t, twice, between the limits t=0 and t=50 (it can be any time interval)
im not sure if the interval for x has to be defined as well.
the equation for displacement is
-----------------------------------------equation for displacement (corrected from
Any help would be appreciated!

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Ameer Hamza
Ameer Hamza 2020-11-15
Are you sure that the equations are correct? The solution you posted does not satisfy the initial conditions.
Generally, such a problem can be solved using the Symbolic toolbox
syms x(t) w A
dxdt = diff(x);
dx2dt2 = diff(x,2);
ode = dx2dt2 == -A*w*sin(dxdt);
cond = [x(0)==pi/4 dxdt(0)==0];
sol = dsolve(ode, cond)
or ode45() can be used for a numerical solution.
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KLETECH MOTORSPORTS
KLETECH MOTORSPORTS 2020-11-15
I actually did use cumtrapz , and i think it worked, unless the logic is wrong:
i mistakenly used x=pi/4. what i should have said was A=pi/4. The amplitude is pi/4.
%this part integrates the acceleration(y1 = d^2(x)/dt^2) twice
% to get both velocity(y2) and displacement(y3)
t=0:0.01:2
w=15.24; %calculated using findwsq.m
A=pi/2;
y1=-A*(w.^2)*sin(w*t); %here y1 is diff(x,t,2) , i.e, accln
y2=cumtrapz(t,y1); %here y2 is diff(x,t) , i.e, velocity
y3=cumtrapz(t,y2); %here y3 is the
y3a= A*sin(w*t); %direct displacement expression
plot(t,y3, t,y3a)
Ameer Hamza
Ameer Hamza 2020-11-15
Yes, in that case, initial conditions will be zero and you can use cumtrapz().

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