Ed asked in 社會與文化語言 · 10 years ago

# MATLAB 問題 (會英文的)

#1:

A parachutist of mass m=68.1kg jumps out of a stationary hot air balloon. The velocity of the parachutist as a function of time is given by the equation: v(t)=gm/c(1-exp(-(c/m)t))

(a) Plot the exact solution of the position as a function of time by integration of v(t) for 0 <=t<=30 with an increment of 1 s. On the same graph, plot the position found by employing the trapezoidal rule to numerically integrate v(t) using an increment of 1 s. Include a legend.

(b) On a second graph, plot the position as a function of time for 0<=t<=30 with an increment of 1 s using the MATLAB quad function. Compare the results to the exact solution. Include a legend.

Try the MATLAB subplot command to place the graphs of parts (a) and (b) in the same graphics window.

Update:

Update 2:

The drag coefficient c is 12.5 kg/s and g is the gravitational constant g=9.81 m/s^2

Update 3:

Rating
• Elisha
Lv 6
10 years ago

看到公式後, 發現公式中的c不知為何? 是一參數嗎? 是否可以給個數值呢?以方便計算

2011-05-16 07:55:34 補充：

clear all

clc

m = 68.1; % kg

c = 12.5; % kg/s

g = 9.81; % m/s^2

% (a)

tspan = 0:1:30;

velocity = g*m/c*(1-exp(-(c/m)*tspan));

% integration by trapezoidal rule

position_t(1) = 0; % assume the height equal to zero at initial point

for k = 1:length(tspan)-1

position_t(k+1) = trapz([velocity(k) velocity(k+1)]);

end

% plot

figure(1)

plot(tspan, velocity, tspan,position_t)

xlabel('time,sec')

ylabel('velocity,m/s')

legend('velocity','position by trapezoidal rule','location','northwest')

% (b)

position_q(1) = 0;

for k = 1:length(tspan)-1

end

% plot

figure(2)

plot(tspan, velocity, tspan,position_q)

xlabel('time,sec')

ylabel('velocity,m/s')

legend('velocity','position by matlab of quad rule','location','northwest')% subplot

figure(3)

subplot(2,1,1)

plot(tspan, velocity, tspan,position_t)

legend('velocity','position by trapezoidal rule','location','southeast')

subplot(2,1,2)

plot(tspan, velocity, tspan,position_q)

legend('velocity','position by matlab of quad rule','location','southeast')

xlabel('time,sec')

ylabel('velocity,m/s')

----------------------------------------------------圖形如下, 我列最後一張

• 10 years ago

試著幫你前半部，剩的你試著自己翻看看（掙扎過才會有進步）

跳傘員質量（即體重）68.1 公斤，從一靜止的熱氣球跳下，該員降落速度與時間的函數關係如公式所述 v(t)=gm/c(1-exp(-(c/m)t))。

(a) 對 v(t) 積分，範圍 0 <=t<=30，以 1 秒(s) 遞增，繪出時間與位置函數關係的正確圖形。在相同的圖上，再利用梯形積分法，對 v(t) 進行數值積分，遞增值同為 1 秒，將求出的位置點連成圖線。請在圖上加上註解文字。

2011-05-15 08:49:33 補充：

這可把我難倒了，我不是理工科的，加上沒學過微積分。

有請此方面的高手岀馬！