Question

A 3-kg mass is attached to a spring with stiffness 81 N/m. The damping constant for the system is 18/3 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 3 m/sec, what is the maximum displacement from equilibrium that it will attain? The maximum displacement is meters (Type an exact answer, using radicals as needed.)

Answer 1

Given ३ m= 3kg K= TINm - 33 Tet displacement द any I then पy 1ve imall + ++ke = 0 the be time the with X(0) - 20 cm 2 20 Too TO | 210) = M 5 and र) = "S A becomes 32 + 1313x + 81x-0

Auxiliary Equation 3m +1253+ 16 2 m+ 63m+27-0 (m +35) m = . - 313, - 353 € Equal srose :: (t) = ( +ct)33t NA 1) 5 -- 5 -353 313t सा: -33c - 33 353t +Cre simee 2017 3 → 32 - 3130 + 3+ 3.3T 32 S C2 3(1) 7 (t) = + 3(1+gg )t) ES

(+10 -3J3t -38te -35 JJt +3 (142) 5. - -3530 3.3 + 3 (+) (1- 331) - 2152) S spree 353€ -3B 5 +3 (+F)(1-315t) 20 मे 3 {+ SY) (1- 3J31 ) - 313 - (1-313t) D 5 5th 1-33ta ने ।- 3 5+3 - 321 S+8 प (55) उनि Jw + 154

| maximum Displacement 15 33x 5 (++ 3 (1) 5 53+9 153+9 53 513+3 365+53) 1573+9 (+ e 5+3 5.3+3 ( 153 53+3 Je 5 कार