Question

Problem 3. A mass m = 0.4 kg is attached to the dashpot with damping coefficient c 5 N and N two springs: k,= 40 and k 20 this system: (a) Derive equation of motion, and determine: Assume that the surface of contact of mass is smooth. For m m K2 (b) Damping factor (ratio) ; (c) Logarithmic decrement 6; (d) System response, x(t) due to initial conditions: x(0) = 20mm, x(0) 0.5 m/sec k1 m

Answer 1

m = 0.4 kg C=5n-sim Kj=LONIM, Kz = 200mm ay writing the Ean of motim mir = -K₂ X _k, 2-cosé y mit că tk tk ₂) a=0 => 0.4ä +58 +(40+20)x=0 - -- 451 +soxt 600x=0 by Damping factor. G= where was vkt kz = 5v5 ls. 1 = 5 :0-204 Cunardamped) - 2x0.4x suf ey Loganithmic decay St S= 21 ly = 1.309. 2mwn -VI-62 - d) System response = for under compeo systems, 26235 60ml { x® cos vo-se wat + si@+ wn Yo Samathalt ust - VT-42 un e-2.5t as it +/500+50 i . Sh12 Scanned with CS Cams XC9) Fer en $20 C0502t) + 4508 Sih(12+)4