You stand on the end of a diving board and bounce to set it into oscillation. You find a maximum response in terms of the amplitude of oscillation of the end of the board when you bounce at frequency f. You now move to the middle of the board and repeat the experiment. Is the resonance frequency for forced oscillations at this point higher, lower, or the same as f?
a concave mirror forms a real image at distance of 25cm for an object distance of 50cm .Calculate the magnification produced by the mirror
Higher
To determine whether the resonance frequency for forced oscillations at the middle of the board is higher, lower, or the same as the frequency f, we need to analyze the behavior of the oscillations.
When you bounce on the end of the diving board, you are performing forced oscillations. By applying a periodic force at frequency f, you are driving the board to oscillate at that same frequency. If the frequency of the driving force matches the natural frequency of the diving board, resonance occurs, leading to a maximum response in terms of the amplitude of oscillation.
When you move to the middle of the board, the dynamics of the oscillation change. At the middle of the board, the board is more rigid and less flexible compared to the end. This increased rigidity affects the natural frequency of the diving board.
In general, when an object's rigidity is increased, its natural frequency also increases. This means that the resonance frequency for forced oscillations at the middle of the board is higher than the frequency f.
Therefore, when you move to the middle of the diving board and repeat the experiment, the resonance frequency for forced oscillations will be higher than f.