For self-locking in screw jacks:
- Friction angle>Helix angle.
- Efficiency must be less than 50%.
- Overhauling occurs if efficiency exceeds 50%.
Step 1: Understanding the self-locking condition. A screw jack is considered self-locking if, when the external effort is removed, the load does not descend on its own. This occurs when the friction angle is greater than the helix angle.
Step 2: Efficiency and self-locking. For a screw jack to be self-locking:
- The efficiency must be less than 50%.
- If the efficiency were greater than 50%, the screw would become overhauling, meaning the load could start descending without external force.
Step 3: Choosing the correct answer.
- (a) Incorrect – Maximum efficiency would lead to overhauling.
- (b) Incorrect – Minimum efficiency does not define self-locking.
- (c) Correct – A self-locking screw jack should not unwind on its own.
- (d) Incorrect – Efficiency must be less than 50% for self-locking.
Thus, the correct answer is (c) It should not unwind to lower the load if left to itself.
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.