Answer:
the range of K can be said to be : -3.59 < K< 0.35
Explanation:
The transfer function of a typical tape-drive system is given by;
![KG(s) = \dfrac{K(s+4)}{s[s+0.5)(s+1)(s^2+0.4s+4)]}](https://tex.z-dn.net/?f=KG%28s%29%20%3D%20%5Cdfrac%7BK%28s%2B4%29%7D%7Bs%5Bs%2B0.5%29%28s%2B1%29%28s%5E2%2B0.4s%2B4%29%5D%7D)
calculating the characteristics equation; we have:
1 + KG(s) = 0
![1+ \dfrac{K(s+4)}{s[s+0.5)(s+1)(s^2+0.4s+4)]} = 0](https://tex.z-dn.net/?f=1%2B%20%20%20%5Cdfrac%7BK%28s%2B4%29%7D%7Bs%5Bs%2B0.5%29%28s%2B1%29%28s%5E2%2B0.4s%2B4%29%5D%7D%20%3D%200)
![{s[s+0.5)(s+1)(s^2+0.4s+4)]} +{K(s+4)}= 0](https://tex.z-dn.net/?f=%7Bs%5Bs%2B0.5%29%28s%2B1%29%28s%5E2%2B0.4s%2B4%29%5D%7D%20%2B%7BK%28s%2B4%29%7D%3D%200)


We can compute a Simulation Table for the Routh–Hurwitz stability criterion Table as follows:
1 5.1 2+ K
1.9 6.2 4K
1.83
0
4K 0
S
0 0


We need to understand that in a given stable system; all the elements in the first column is usually greater than zero
So;
11.34 - 1.9(X) > 0


7.54 +2.1 K > 0
2.1 K > - 7.54
K > - 7.54/2.1
K > - 3.59
Also
4K >0
K > 0/4
K > 0
Similarly;
XY - 7.32 K > 0
![(\dfrac{3.8+1.9K-4K}{1.9})[11.34 - 1.9(\dfrac{3.8+1.9K-4K}{1.83}) > 7.32 \ K]](https://tex.z-dn.net/?f=%28%5Cdfrac%7B3.8%2B1.9K-4K%7D%7B1.9%7D%29%5B11.34%20%20-%201.9%28%5Cdfrac%7B3.8%2B1.9K-4K%7D%7B1.83%7D%29%20%3E%207.32%20%5C%20K%5D)
0.54(2.1K+7.54)>7.32 K
11.45 K < 4.07
K < 4.07/11.45
K < 0.35
Thus the range of K can be said to be : -3.59 < K< 0.35
Answer:
The lift coefficient is 0.3192 while that of the moment about the leading edge is-0.1306.
Explanation:
The Upper Surface Cp is given as

The Lower Surface Cp is given as

The difference of the Cp over the airfoil is given as

Now the Lift Coefficient is given as

Now the coefficient of moment about the leading edge is given as

So the lift coefficient is 0.3192 while that of the moment about the leading edge is-0.1306.
Answer: (a) +/- 7.5° (b) +/- 3.75°
Explanation:
See attachment
Answer:
(a) the percent thermal efficiency is 27.94%
(b) the temperature of the cooling water exiting the condenser is 31.118°C
Explanation: