作者terrylove12 (风馡)
看板Grad-ProbAsk
标题[理工] [工数]-ODE问题
时间Sat Jan 9 23:49:41 2010
题目是成大水利96年考题
An object having mass "m" falls from rest toward the earth from a grate height
under the gravity force with acceleration "g". As it falls, air resistance
acts upon it, and this resistance "Fd" is proportional to the square of the
velocity V, i.e., Fd=α(V^2) . According to the Newton's second law, the
equation of motion for falling object can be written as
dv
m─ = mg -α(V^2) with V(0)=0
dt
Please find the velocity V(t) and the terminal velocity V∞ that is the
velocity at the time approaching infinite.
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 114.36.20.219
1F：推 abcxyz123:分离变数 积分 01/10 00:00
2F：→ terrylove12:dv=gdt-[α(V^2)/m]dt V平方项 可以请问怎麽丢过去吗 01/10 00:16
3F：→ terrylove12:如果丢过去变成 V^(-2)dv=V^(-2)gdt-(α/m)dt 01/10 00:18
4F：→ terrylove12:还是不能变数分离ˊˋ 还是我有错误的地方呢 01/10 00:18
5F：→ terrylove12:喔喔 找到方法了 但是积分过程很复杂 01/10 00:33
6F：推 ntust661:很平常的运动方程式@@ 01/10 03:41