Frequency away from an oscillating body

In summary, a physics student stands on a wooden plank placed over a 5.00 m wide pit and jumps upward two times per second, causing the plank to oscillate with a large amplitude. Part A asks for the speed of transverse waves on the plank, which is 20m/s. In Part B, the student is standing 1.25 m from the edge of the pit and is asked for the rate at which she must jump to produce large-amplitude oscillations. This requires understanding of harmonics, as different jumping rates at different distances from the pit will produce different standing wave patterns on the plank. The correct jumping rate for large-amplitude oscillations has not been determined yet.
  • #1
roberttk01
3
0
This is the set up to the question that we got for homework:

Pit and Plank. A wooden plank is placed over a pit that is 5.00 m wide. A physics student stands in the middle of the plank and begins to jump up and down such that she jumps upward from the plank two times each second. The plank oscillates with a large amplitude, with maximum amplitude at its center.

Part A) Asks :
What is the speed of transverse waves on the plank? Answer: 20m/s

Part B)
At what rate does the student have to jump to produce large-amplitude oscillations if she is standing 1.25 m from the edge of the pit? (Note: The transverse standing waves of the plank have nodes at the two ends that rest on the ground on either side of the pit.)


-Part B is where I am having issues. I tried using the added length and the same speed, the offset length and same speed, and the original length minus the new length with the same speed and nothing has produced what it is looking for. Please help?
 
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  • #2
Harmonics, perhaps?
 

1. What is frequency away from an oscillating body?

Frequency away from an oscillating body refers to how far away an object or system is from its natural frequency of oscillation.

2. How is frequency away from an oscillating body measured?

Frequency away from an oscillating body is typically measured in Hertz (Hz), which is the number of oscillations per second. It can also be expressed in radians per second (rad/s).

3. What factors affect the frequency away from an oscillating body?

The frequency away from an oscillating body can be affected by factors such as the mass, stiffness, and damping of the system. Changes in these parameters can cause the natural frequency to shift.

4. How does frequency away from an oscillating body impact the behavior of the system?

The frequency away from an oscillating body can significantly impact the behavior of the system. If the system is operating at its natural frequency, it will experience resonance, which can lead to excessive vibrations and potential damage. If the frequency is significantly different from the natural frequency, the system may not function properly or efficiently.

5. How can frequency away from an oscillating body be controlled or adjusted?

The frequency away from an oscillating body can be controlled or adjusted by changing the mass, stiffness, or damping of the system. This can be achieved through design modifications or using external devices such as dampers or tuned mass dampers. It is essential to carefully consider and analyze the system's dynamics to determine the best approach for controlling the frequency away from an oscillating body.

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