For each function , sketch the Bode asymptotic magnitude and asymptotic phase plots. a. G(s)= 1/s(s+2)(s+4)
b. G(s)= (s+5)/(s+2)(s+4)
c. G(s)= (s+3)(s+5)/s(s+2)(s+4)

attached below

Explanation:

a) G(s) = 1 / s( s+2)(s + 4 )

Bode asymptotic magnitude and asymptotic phase plots

attached below

b) G(s) = (s+5)/(s+2)(s+4)

phase angles = tan^-1 w/s , -tan^-1 w/s , tan^-1 w/4

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c) G(s)= (s+3)(s+5)/s(s+2)(s+4)

solution attached below

The omitted part of the question shown in bold format

The lead of the threaded shaft of the C-clamp is 0.05 in., and the mean radius of the thread is r = 0.15 in. Assume μs = 0.18 and μk = 0.16. What couple must be applied to the shaft to exert a 30-lb force on the clamped object?

C = 0.967 in. lb

Explanation:

Given that:

The lead of the threaded shaft of the C-clamp is 0.05 in.

∴ the pitch of the screw = 0.05 in

the mean radius of the thread is r = 0.15 in.

Assuming:

(μs)= 0.18  which implies the  coefficient of the static friction

(μk) = 0.16  (coefficient of kinetic friction)

Force = 30-lb

What couple must be applied to the shaft to exert a 30-lb force on the clamped object?

To determine the Couple (C) that must be applied; we use the expression:

C = Fr  tan ( + )

where; F = force

r =  mean radius

= angle of kinetic friction

= pitch angle

NOW, let's take then one after the other.

From the coefficient of the static friction and the kinetic friction; we can solve for their respective angles, so we have:

Angle of static friction ()  

() =

() = 10.204°

Angle of kinetic friction ()  

= 9.0903°

To determine the pitch angle(); we apply the expression:

() =

() =

() =

() = 3.0368°

Have gotten our parameters to solve for Couple (C); then we have:

C = Fr  tan ( + )

substituting our values; we have:

C = (30 × 0.15)  tan ( 9.0903 + 3.0368)

C = 4.5  × tan ( 12.1271)

C = 4.5  × 0.2148761968

C = 0.96669428854 in.lb

C = 0.967 in. lb

Therefore, 0.967 in. lb couple  must be applied to the shaft to exert a 30-lb force on the clamped object.