Question: (a) Prove that the second-order system whose characteristic polynomial is ms2 + cs + k is stable if and only if m, c, and k

(a) Prove that the second-order system whose characteristic polynomial is ms2 + cs + k is stable if and only if m, c, and k have the same sign,
(b) Derive the conditions for neutral stability.

Step by Step Solution

★★★★★

3.30 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The system is stable if both of its roots are real and negative or if the roots are complex with n... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

755-C-D-S-D (103).docx

120 KBs Word File

Students Have Also Explored These Related Classical Dynamics Of Particles Questions!

(a) Prove that the value of a determinant all of whose elements below the principal diagonal are zero is equal to the product of the diagonal elements. (Such a determinant is called upper...

For a matrix of order 20 whose eigenvalues are 1, 2, 3, ( ( ( ( 20, the characteristic equation can be written as (20m=1 (( - m) = 0, where the product notation is defined by (nk=1 bk ( b1b2( ( (bn....

(a) Prove that the zero vectors (0, 0, 0, 0) has these same components in all reference frames. (b) Use (a) to prove that if two vectors have equal components in one frame, they have equal components...

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

John Ohnesorge 2016'The Regulatory State in East Asia'in Comparative Law and Regulation 92-106. Please refer to the attachments. 3. The regulatory state in East Asia they are gi judgment. F John...

A discrete sequence {xn} can be converted into a continuous representation x(t) = ts X n= (t n ts) xn, where ts is the sampling period. (a) State two characteristic properties of Dirac's function. [2...

Prove it for second-order PDEs in two and three independent variables. Prove it by substitution.

Given the generators $X_{a}$ (with $a=1, \ldots, N$ ) of a Lie algebra, prove that the second-order Casimir operator $C^{(2)}=\sum_{a=1}^{N} X_{a} X_{a}$ commutes with all the generators.

Audit the segment on Sarbanes-Oxley (26-1a) and the informant prerequisites in the Securities Exchange Act of 1934. 1. Under Sarbanes-Oxley, list the three occasions that a reviewer would have to...

A zoologist collected wild lizards in the Southwestern United States. Thirty lizards from the genus Phrynosoma were placed on a treadmill and their speed measured. The recorded speed (meters/second)...

Organizational culture plays a crucial role in shaping the behavior, attitudes, and performance of employees within an organization. As a leader, how can you create and nurture a positive...

Indicate with a S or W if the following is a Strength or Weakness: The use of pre-numbered purchase orders Question 2 (1 point) ) Listen A Indicate with a S or W if the following is a Strength or...

12.44 Refer to Example 11. Ignore the covariate original reflectivity. Perform an analysis of variance take = 0.05

Use MATLAB to plot the polynomial y = 3x 4 - 5x 3 - 28x 2 - 5x + 200 on the interval $1 x 1. Put a grid on the plot and use the ginput function to determine the coordinates of the peak of the curve.

Use MATLAB to find the following product: (10x 3 - 9x 2 - 6x + 12)(5x 3 - 4x 2 - 12x + 8)

Use MATLAB to find the quotient and remainder of 143 ? + 3 + 9 5x? + 7x 4

What is the present worth of all disbursements and receipts during the life time of the project, evaluated at the beginning of the first year, if the project has the following costs: Phase 1 labor...

Can someone explain this question with working for me please. 4. Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 196. The distribution of...

Suppose that you can got a 30-year mortgage at 8% interest. How much can you afford to borrow if you can afford to make a monthly payment of $1,000