Question

6-B) A weight attached to a spring of stiffness 982 N/m has a viscous damping device. When the weight is displaced and released, the period of vibration is 1.02 s, and the magnitude of consecutive amplitudes is 0.61 m and 0.29 m. a) Identify the mass (m) and damping (c) coefficient. b) Determine the amplitude and phase of the response when a force, f(t) = 4.2 cos (6.31) N, acts on the system.

Answer 1

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Given data, K: 982 mm; lo 0.29 Ta 0.61; Xl Xo 1.025. Il ç.wn. Te. e a) we have, Ho 지 or after simplying above relation , we we get 8 = aliq in( ) = vi-G2 finding '' from above equation. 0.74 arę . vier. (0.74) ? (1-qr] =451. go (8.44)? & 2 ((0.74) = 45 +4ū aus 0-1169

We have; Wd : wn. 1-G2 211 Si wn. 1 -&? Tai Wn 6.2 (6-2) K 17 K m. m. ma 982 ll 25.54 kg (6-2)2 0.1169 С. C aus = = ulu со Kom. c= 0.1169 x 2.X 982 XQ5-54 37-02 N-5/m. c = b ) . mut căit Ka= F. = 4.2 Co8(636) General Equation for forced vibration. Compare: Fa Fo.cos(wt) A Sin cat-) Response: xlt)

Fo - 462 4.d. i wa 6-3 gads Amplit tude (A) = (Folk) 2 (@Jaceste (42/aer) (-03) + (vegesen = a 2 As O-0178 m. tand = wo (25.95 1-( $ - town (-on) wn V 82.21€.