Second Order System Analysis

This video tutorial covers the analysis of a second-order system using its transfer function. It begins with an introduction to the problem, followed by a comparison of the given system with the standard form to derive omega and zeta values. The tutorial then calculates transient specifications such as rise time, peak time, and peak overshoot. Finally, it addresses the settling time and derives the output response c(t) for a unit step input.

What is the main focus of the video tutorial?

• Introduction to first order systems

• Discussion on third order systems

• Analysis of second order systems

• Overview of control systems

What is the transfer function given in the problem statement?

• 20 by s^2 + 8s + 20

• 15 by s^2 + 4s + 15

• 25 by s^2 + 6s + 25

• 10 by s^2 + 5s + 10

What is the standard form of a second order system?

• omega n^2 by s^2 + 2zeta omega n s + omega n^2

• omega n by s + zeta omega n

• omega n by s^2 + zeta omega n s

• omega n^2 by s + zeta omega n

How is omega n calculated from the given transfer function?

• Square root of 6

• Square root of 25

• Square root of 36

• Square root of 49

What is the formula for omega d?

• omega n into 1 - zeta^2

• omega n into zeta^2

• omega n into 1 - zeta

• omega n into 1 + zeta^2

What is the formula for calculating rise time?

• theta by omega d

• pi minus theta by omega d

• pi by omega d

• omega d by pi

How is peak time calculated?

• pi by omega d

• pi minus theta by omega d

• theta by omega d

• omega d by pi

What is the formula for peak overshoot?

• e power minus pi zeta by 1 minus zeta^2

• e power pi zeta by 1 minus zeta^2

• e power minus pi zeta by 1 plus zeta^2

• e power pi zeta by 1 plus zeta^2

What is the formula for settling time?

• 2 by zeta omega n

• 6 by zeta omega n

• 4 by zeta omega n

• 8 by zeta omega n

What is the expression for the output response c(t)?

• 1 plus e power zeta omega n t by sqrt(1 minus zeta^2) into sine(omega d t + theta)

• 1 minus e power minus zeta omega n t by sqrt(1 minus zeta^2) into sine(omega d t + theta)

• 1 plus e power minus zeta omega n t by sqrt(1 minus zeta^2) into sine(omega d t + theta)

• 1 minus e power zeta omega n t by sqrt(1 minus zeta^2) into sine(omega d t + theta)