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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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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 Nm1 c = 650 Nsm1 , L = 1.2 m and the mass of the bar is 15kg.

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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(1r2)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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