[討論] 普物作業~

[after17s (專業代PO~"~)]

         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)
→ after17s:p.s 答案都不確定...
推 ivycheng1120:第七版的課本是這題...可是課本答案只提供奇數題的