[问答题]
1.An engineer designs a bridge. By using software, they simulate how the amplitude A of the vibration of the bridge varies with the driving frequency $f$ of vibration due to wind.
To avoid resonance, they decided to increase the amount of damping by changing the design of the bridge.
（1）State the difference between forced and free vibrations.
（2）Explain why resonance is dangerous for bridges.
（3）On the graph below, sketch the variation of the amplitude of the vibration of the bridge with the frequency of the forced vibration after the damping is increased.
There is no need to add values to the axes
Dashed lines are showing the graph before the damping is increased
（4）In some cases, resonance can be useful. Describe a practical application of resonance.
2.A restaurant uses a swinging door to provide a convenient way for people to move in and out.
Identify the damping type of the door if the door:
（1）swings back very slowly and returns to the closed position without oscillating.
（2）swings back and forth several times before reaching the closed position.
（3）closes smoothly in a short time and does not oscillate back and forth before coming to a stop.
