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A moment Mosin wt is applied to the end of the end of the bat of figure.
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written 5.8 years ago by |
Determine the maximum value of Mo such that the steady state amplitude of angular oscillation does not exceed 10˚ if w = 500 rpm, k = 7000 Nm−1 c = 650 Nsm−1 , L = 1.2 m and the mass of the bar is 15kg.
1] w = 0π×50060 = 52.35 rad/sec
KE = 12Io ˙θ2
=12 [mL212 + m (L4)2]˙θ2
Ieq = mL212 + ml216
Ieq = 0.145 mL2
= 3.15 m4
2] PE = (PE)LS + (PE)RS
=12 K (14θ)2 + 12×2k×(3L4θ)2
Keq = [Kl216 + 18kL216]
=kL216 + 9kL28
Keq = 11970 N/m
3] Wn = √KeqIeq = 61.64 rad/sec
4] W.D = −∫ t c.˙y dy
=−∫ c. (L4θ) d (L4θ)
Ceq = cL216
Ceq = 58.5Nsm
ξ = CeqCceq=cL2/162Ieq Wn=0.1506
r=wwn=52.3565.38=0.849
5] θst=MoKeq
θst= 11970 = Mo
6] θθst=1√(1−r2)2 + (2ξr)2
0.174θst = 1√(1−(0.8)2) + (2×0.1306×0.8)2
θst=0.064rad
Mo = 76 7. 36 N-m
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