Question

Would appreciate any help. Will upvote.

3.6.18 Draw a second spring and mass hanging from the first. If the masses are mq,m2 and the spring constants are C1,C2, the energy is H =K+P = 2m, ri + zimą på + 3c, ut + czlu – u,s?. Find the four Hamilton's equations OH/Op; = du;/dt,8H/du;= – dp:/dt, and the matrix equation Mu" + Ku=0.

Answer 1

Ho k+P = I piatto. Pe? + < CUP to C2(02-01). 2m2 m2 consider, ƏH/39,- tipit lo) - Pl/m, = alle and = str. Apz = P2 at ap2 m2 m2 consideran Hai che non 191. fuit+s 42.98 02-01) (-1) = code CIUL - CaCuz-01) - - & dpi = C2 (02-01) - CIUI considers alaus = - det * $69.4602-01) - do o t hey coco-os)]

Four Hamilton equation a au2 at dp = Pz ma = CaCU2-0,7 - GIUL dt . dP - Cocom-02) consider consider, dus efet pas me dpn C2 (U2 - 0,) - CIUI -(1) det - - C2(02-01) -c) de incis en e detit - CIVI dt substitute dt -ciul de todo en Dit malone Pu- ma ei tea : + at (m, archite) + est ) --CIVI 2 + m2 a + CIU -O mi 224 at2 Ot2 which is of the form Mu" + ku=0.