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標題:

Applied Maths - Mechanics 48

發問:

A particle moves in a plane with an acceleration which is parallel to the axis of y and varies as the distance from the axis of x. Show that(a) when the acceleration is a repulsion, the equation of its path is y = Aa^x + Ba^(-x) ,(b) when the acceleration is attractive, the equation of its... 顯示更多 A particle moves in a plane with an acceleration which is parallel to the axis of y and varies as the distance from the axis of x. Show that (a) when the acceleration is a repulsion, the equation of its path is y = Aa^x + Ba^(-x) , (b) when the acceleration is attractive, the equation of its path is y = Acos(ax + B) .

最佳解答:

• help help各位改名問題
• 我41(kg),150cm,係唔係好肥-(女,11歲)
• ue依個分應該e or f機會大呀-

• help help各位改名問題
• 我41(kg),150cm,係唔係好肥-(女,11歲)
• ue依個分應該e or f機會大呀-

 

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(a) d2x/dt2 = 0 => x = pt + q or t = (x – q)/p where p and q are constants d2y/dt2 = k2y => y = mekt + ne-kt where k, m and n are constants y = mek(x – q)/p + ne-k(x – q)/p y = me-kq/pekx/p + nekq/pe-kx/p y = me-kq/p(ek/p)x + nekq/p(ek/p)-x Combining constants A = me-kq/p; B = nekq/p; a = ek/p y = Aax + Ba-x (b) d2y/dt2 = - k2y => y = mcos kt + nsin kt where m and n are constants Let tan s = n/m then sin s = n/√(m2 + n2); cos s = m/√(m2 + n2) y = √(m2 + n2) (cos kt cos s + sin kt sin s) y = √(m2 + n2)cos(kt – s) y = √(m2 + n2)cos[k(x – q)/p – s] y = √(m2 + n2)cos(kx/p – kq/p – s) Combining constants A = √(m2 + n2); a = k/p; B = -kq/p – s y = Acos(ax + B)

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