Question

6.3 Consider a double mass-spring system with two masses of M and m on a frictionless surface, as shown in Figure 6.30. Mass m is connected to M by a spring of constant k and rest length lo. Mass M is connected to a fixed wall by a spring of constant k and rest length lo and a damper with constant b. Find the equations of motion of each mass. (HINT: See Tutorial 2.1.) risto M wa ww W m . Figure 6.30 Problem 6.3.

Question 6.3

Answer 1

(6.3) let at any time't situation is as shown in fg. ---> x and a care functions of time. That is x= x (t) and a=2(t) Amount of stretch in spring connected between masses M andm = a(t)- X(t)-do Amount of Stretch in spring between wall and mals m = X(t) do For mais 'n R(x-x-lo) Mofron along honzontal line de me = ~R EX +2 _lo) -motion d. 24 = -K (x(+1+r(t)-60) EM . for merés'm' m7 bit) For mass n' flence equation of mofton is R(x4) do) F k ( xft) _ X(t) _do) q.xt) = - R (X(t) –Lo) – b «[4) + R/36t )-x(+)-lo) = -bxct) - RTX) -lo - Alt) + X[t ) +do] -RT heat of wat Equation of motion