In a free damped vibrating system, the amplitude:
a) Increases with time
b) Decreases with time
c) Remains constan
d) Oscillates randomly
The correct answer and explanation is:
The correct answer is b) Decreases with time.
In a free damped vibrating system, the amplitude decreases over time due to the energy lost to the surrounding medium, such as air resistance or internal friction within the system. Damping refers to the effect that reduces the oscillation’s amplitude as the system dissipates energy. This dissipation occurs as the mechanical system moves through a resistive medium, which causes a gradual loss of kinetic energy with each oscillation cycle.
There are different types of damping, such as viscous, Coulomb, and hysteresis damping, but in all these cases, the overall effect is the same: the amplitude of oscillation decreases over time. The system loses energy to the medium it moves through, and this energy loss results in a reduction in the motion of the system. In a viscous damping system, for example, the resistive force is proportional to the velocity of the oscillating object, and it works to slow down the motion, gradually diminishing the amplitude until the system eventually comes to rest.
The rate at which the amplitude decreases depends on the level of damping. In the case of underdamped systems, the amplitude decreases slowly, and the system continues to oscillate for a longer period before eventually stopping. In critically damped and overdamped systems, the system returns to equilibrium without oscillating, but in the case of free damping, there will still be oscillations, albeit with diminishing amplitude over time.
Therefore, a free damped system is characterized by the gradual decrease in amplitude, and this effect is inevitable unless external energy is added to counterbalance the damping forces.