Vibrations

Step 1: Understanding vibration behavior.
In vibration systems, amplitude may remain constant or decrease depending on energy loss mechanisms such as friction or damping.
Step 2: Effect of damping.
When damping is present, energy is dissipated in every cycle, causing the amplitude to reduce progressively with time.
Step 3: Eliminating incorrect options.
Free vibration occurs without external force but may or may not include damping.
Forced vibration occurs due to continuous external excitation.
Underdamped vibration is a specific case of damped vibration with oscillations present.
Step 4: Conclusion.
A reduction in amplitude over each cycle indicates damped vibration.

Step 1: Understanding critical damping.
Critical damping is the minimum amount of damping required for a system to return to its equilibrium position without oscillation in the shortest possible time.
Step 2: Expression for critical damping.
For a single degree of freedom system, the critical damping coefficient is given by: where is the mass of the system and is the stiffness.
Step 3: Identifying dependent parameters.
From the expression, it is clear that critical damping depends only on mass and stiffness of the system.
Step 4: Conclusion.
Hence, critical damping is a function of mass and stiffness.