作者after17s (專業代PO~"~)
看板CSMU-PT97
標題[討論] 普物作業~
時間Wed Dec 10 16:55:38 2008
題目:
The suspension system of a 2000kg automobile "sags"
10cm when the chassis is placed on it. Also, the
oscillation amplitude decreases by 50% each cycle.
Estimate the values of (a) the spring constant k and
(b) the damping constant b for the spring and shock
absorber system of one wheel, assuming each wheel
supports 500kg.
物理作業是這一題嗎!!!!?
(a)constant k=?
F=-kx
=> m*g=-kx
=>500kg*10=-k*(-0.1m)
=> k=5*10^4 N/m
(b)damping constant b=?
x(t)=Ae^(-αt)cosω't
x(0)=A ....(1)
x(T)=0.5A=Ae^(-αT)cosω'T ....(2)
p.s{T=2π√(m/k)=2π/ω' α=b/2m A=0.1cm}
=> 由(1)(2)得知
=> e^(-αT)cosω'T=1/2 cosω'T=cos2π=1
=> (-αT)=In(1/2) 左右兩邊同時取以自然對數e為底之log
=> {-[b/2m]*[2π√(m/k)]}=In(1/2)=-0.7
2m*0.7 2*500*0.7
=> b= ─────── = ──────────
2π√(m/k) 2*3.14*√500/5*10^4
700
= ─────── = 1114.65 kg/s
2*3.14*0.1
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※ 編輯: after17s 來自: 122.127.0.169 (12/10 22:48)
1F：→ after17s:p.s 答案都不確定... 12/10 22:52
2F：推 ivycheng1120:第七版的課本是這題...可是課本答案只提供奇數題的 12/11 00:55