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A diving board oscillates with simple harmonic motion of frequency 2.5 cycles per second. What is the maximum amplitude with which the end of the board can oscillate in order that a pebble placed there (Fig. 40$)$ does not lose contact with the board during the oscillation?

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$$4.0 \mathrm{cm}$$

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

University of Michigan - Ann Arbor

Simon Fraser University

University of Winnipeg

McMaster University

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

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In physics, an oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The oscillation may be periodic or aperiodic.

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so here the maximum downwards acceleration has to be equal to gravity because the board, of course, cannot move faster than the pebble. If the pebble on the board do not want to lose contact with one another, so the maximum acceleration would be equal, rather would be equal to four pies square times the frequency squared times the amplitude and this has to be less than G. Therefore, the amplitude must be less than or equal to this acceleration due to gravity divided by four pi squared times, the frequency squared. And so uh, we can say that the amplitude must be less than or equal to on 9.8 meters per second squared, divided by four pi squared times the frequency of 2.5 hertz squared and we find that the amplitude cannot be has to be less than or equal to 0.397 meters. So this would be Earth answer that is tthe e end of the solution. Thank you for watching

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