All of the above
Step 1: Understanding molecular vibrations. - Molecular vibrations are categorized into stretching and bending. - Bending vibrations include scissoring, rocking, wagging, and twisting.
Step 2: Explanation of bond angle changes in bending vibrations.
- Scissoring: Involves movement of atoms towards or away from each other, changing the bond angle.
- Twisting: A torsional motion where one part of the molecule moves opposite to another, changing the bond angle.
- Rocking: Movement occurs in the plane but does not change bond angles.
Step 3: Explanation of incorrect options.
- (A) Scissoring: Incorrect, as it changes bond angles.
- (B) Twisting: Incorrect, as it involves torsional deformation.
- (D) All of the above: Incorrect, as only rocking keeps the bond angle constant.
Step 4: Selecting the correct option. Since rocking vibration keeps the bond angle unchanged, the correct answer is (C) Rocking.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.