Using MATLAB to do Numerical Differentiation
Given: A piecewise function where v(t)=70t @ t<=20s & 1596.2-9.81t @ 20<t<=t_max <—(eq 1)
Also given: s(t)=35t^2+7620 @ t<=20s & 1596.2t-4.905t^2-8342 @ 20<t<=t_max <—(eq 2)
Find: For figure 3 I need to plot my velocity as a function of time, (the same thing I did in figure 1), only this time I need to add an additional line which is the derivative approximation of velocity. I’ll use circle markers for my approximation at every 10th point wtih no line. This is to show that my line for the derivative approximation should be nearly identical to my equation line.
My Solution:
%% Finding Value of tmax
% Finding tmax and rounding it to the nearest whole number
%%
tmaxr=roots([-9.81, 1596.2]);
tmax=ceil(tmaxr);
%% Plotting Equation 1
% Creating Figure 1 from Equation 1
%%
t=0:0.1:tmax;
v=zeros(size(t));
for N=1:length(t)
if t(N)<=20
v(N)=70*t(N);
else
v(N)=1596.2-9.81*t(N); % Only valid for t > 20 seconds
end
end
figure(1)
plot(t,v)
xlabel(‘Time (s)’)
ylabel(‘Velocity (m/s)’)
title(‘Velocity vs. Time’)
%% Plotting Equation 2
% Creating Figure 2 from Equation 2
%%
t=0:0.1:tmax;
s=zeros(size(t));
for N=1:length(t)
if t(N)<=20
s(N)=35.*t(N).^2+7620;
else
s(N)=1596.2.*t(N)-4.905.*t(N).^2-8342;
end
end
figure(2)
plot(t,s)
xlabel(‘Time (s)’)
ylabel(‘Altitude (m)’)
title(‘Position vs. Time’)
Issue: So I have the above code which I believe to be correct but not sure of how to get the derivative approximation…Given: A piecewise function where v(t)=70t @ t<=20s & 1596.2-9.81t @ 20<t<=t_max <—(eq 1)
Also given: s(t)=35t^2+7620 @ t<=20s & 1596.2t-4.905t^2-8342 @ 20<t<=t_max <—(eq 2)
Find: For figure 3 I need to plot my velocity as a function of time, (the same thing I did in figure 1), only this time I need to add an additional line which is the derivative approximation of velocity. I’ll use circle markers for my approximation at every 10th point wtih no line. This is to show that my line for the derivative approximation should be nearly identical to my equation line.
My Solution:
%% Finding Value of tmax
% Finding tmax and rounding it to the nearest whole number
%%
tmaxr=roots([-9.81, 1596.2]);
tmax=ceil(tmaxr);
%% Plotting Equation 1
% Creating Figure 1 from Equation 1
%%
t=0:0.1:tmax;
v=zeros(size(t));
for N=1:length(t)
if t(N)<=20
v(N)=70*t(N);
else
v(N)=1596.2-9.81*t(N); % Only valid for t > 20 seconds
end
end
figure(1)
plot(t,v)
xlabel(‘Time (s)’)
ylabel(‘Velocity (m/s)’)
title(‘Velocity vs. Time’)
%% Plotting Equation 2
% Creating Figure 2 from Equation 2
%%
t=0:0.1:tmax;
s=zeros(size(t));
for N=1:length(t)
if t(N)<=20
s(N)=35.*t(N).^2+7620;
else
s(N)=1596.2.*t(N)-4.905.*t(N).^2-8342;
end
end
figure(2)
plot(t,s)
xlabel(‘Time (s)’)
ylabel(‘Altitude (m)’)
title(‘Position vs. Time’)
Issue: So I have the above code which I believe to be correct but not sure of how to get the derivative approximation… Given: A piecewise function where v(t)=70t @ t<=20s & 1596.2-9.81t @ 20<t<=t_max <—(eq 1)
Also given: s(t)=35t^2+7620 @ t<=20s & 1596.2t-4.905t^2-8342 @ 20<t<=t_max <—(eq 2)
Find: For figure 3 I need to plot my velocity as a function of time, (the same thing I did in figure 1), only this time I need to add an additional line which is the derivative approximation of velocity. I’ll use circle markers for my approximation at every 10th point wtih no line. This is to show that my line for the derivative approximation should be nearly identical to my equation line.
My Solution:
%% Finding Value of tmax
% Finding tmax and rounding it to the nearest whole number
%%
tmaxr=roots([-9.81, 1596.2]);
tmax=ceil(tmaxr);
%% Plotting Equation 1
% Creating Figure 1 from Equation 1
%%
t=0:0.1:tmax;
v=zeros(size(t));
for N=1:length(t)
if t(N)<=20
v(N)=70*t(N);
else
v(N)=1596.2-9.81*t(N); % Only valid for t > 20 seconds
end
end
figure(1)
plot(t,v)
xlabel(‘Time (s)’)
ylabel(‘Velocity (m/s)’)
title(‘Velocity vs. Time’)
%% Plotting Equation 2
% Creating Figure 2 from Equation 2
%%
t=0:0.1:tmax;
s=zeros(size(t));
for N=1:length(t)
if t(N)<=20
s(N)=35.*t(N).^2+7620;
else
s(N)=1596.2.*t(N)-4.905.*t(N).^2-8342;
end
end
figure(2)
plot(t,s)
xlabel(‘Time (s)’)
ylabel(‘Altitude (m)’)
title(‘Position vs. Time’)
Issue: So I have the above code which I believe to be correct but not sure of how to get the derivative approximation… plotting, calculus MATLAB Answers — New Questions