Use Routh's stability criterion to determine how many roots with positive real parts the following equations have:
1 answer:
Answer:
a) no roots not in LHP
b) 2 roots not in LHP
c) 2 roots not in the LHP
d) 2 roots not in the LHP
e) 2 roots not in LHP
Explanation:
No roots not in the LHP
2 roots not in the LHP
There are roots in the RHP (not all coefficients are greater than 0).
2 roots not in the LHP
There are two sign changes in the first column of the Routh array.
2 roots not in the LHP
2 roots not in LHP
check:
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Answer:
the required diameter of the rod is 9.77 mm
Explanation:
Given:
Length = 1.5 m
Tension(P) = 3 kN = 3 × 10³ N
Maximum allowable stress(S) = 40 MPa = 40 × 10⁶ Pa
E = 70 GPa = 70 × 10⁹ Pa
δ = 1 mm = 1 × 10⁻³ m
The required diameter(d) = ?
a) for stress
The stress equation is given by:
A is the area = πd²/4 = (3.14 × d²)/4
Substituting the values, we get
d = (9.77 × 10⁻³) m
d = 9.77 mm
b) for deformation
δ = (P×L) / (A×E)
A = (P×L) / (E×δ) = (3000 × 1.5) / (1 × 10⁻³ × 70 × 10⁹) = 0.000063
d² = (4 × A) / π = (0.000063 × 4) / 3.14
d² = 0.0000819
d = 9.05 × 10⁻³ m = 9.05 mm
We use the larger value of diameter = 9.77 mm