Which of the following statements about a system in resonance is true
A.The energy of the system is always increasing.
B.The greater the damping the larger the amplitude of the oscillations
C.The driving force is always in the direction of the velocity.
D.The frequency of the driving force is the same as the natural frequency of the system.
The correct statement is:
D. The frequency of the driving force is the same as the natural frequency of the system.
Resonance occurs in a system when the frequency of the driving force matches the natural frequency of the system. This leads to a maximum transfer of energy between the driving force and the system, resulting in significant oscillations and amplification of the system's response.
To determine which of the statements about a system in resonance is true, let's analyze each option:
A. The energy of the system is always increasing: This statement is not true. In a system in resonance, the energy of the system is transferred back and forth between the potential energy (stored energy) and the kinetic energy (energy of motion), resulting in oscillations. The total energy in the system remains constant, as long as no energy losses occur due to damping or external factors.
B. The greater the damping, the larger the amplitude of the oscillations: This is not true. Damping refers to the dissipation of energy in the system, typically resulting in a decrease in the amplitude of the oscillations. Therefore, the greater the damping, the smaller the amplitude of the oscillations.
C. The driving force is always in the direction of the velocity: This statement is not necessarily true. In a system in resonance, the driving force is applied at the natural frequency of the system, which can lead to vibrations with large amplitudes. However, the direction of the driving force depends on its phase relationship with the displacement of the system. If the phase relationship is in phase, the driving force and the velocity would be in the same direction. If they are out of phase, the driving force and the velocity would be in opposite directions.
D. The frequency of the driving force is the same as the natural frequency of the system: This statement is true. Resonance occurs when the driving force applied to a system matches its natural frequency. When the driving frequency matches the natural frequency, the amplitude of the oscillations becomes significantly larger than under other driving frequencies.
So, the correct answer is D. The frequency of the driving force is the same as the natural frequency of the system.