# Simple Harmonic Motion - HELP

1. Aug 21, 2006

### Lethal

When an elastic spring is stretced beyond its natural unstretched length, a tension exists in the spring creating simple harmonic motion. The magnitude of the tension is given by the experimental law credited to Robert Hooke. Hooke's law states that the tension is directly proportional to the extension of the spring beyond its natural length i.e.,

T = k x

In this expression, T denotes the tension measured in Newtons, and x the extension beyond the natural length of the spring. The constant of proportionality, referred to as the spring constant, describes the stuffness of the spring and is stated in Netwons/metre.

Using Simple Harmonic Motion to model Bungee Jumping.

New Zealand is the home of bungee jumping. One of the major jumps is located on a bridge over the shotover river near Queenstown. This bridge is 71mabove the river.

Two types of jumps are available wet and dry. In a dry jump, the person's fall ends just above the water surface. In a wet jump the person is submerged to a depth of 1 metre.

Participants jump from the bridge, fastened to an elastic rope that is adjusted to half their descent at an appropiate level.

The rope is specially designed and its spring constant is known from specifications. For the purposesof this problem, we will assume that the rope is stretched to twice its normal length by a person of mass 75 kg, hanging at rest from the free end. It is necessary to adjust the length of the rope in terms of the weight of the jumper.

1. For a person of mass m kg, calculate the depth to which a person would fall if attacted to a rope of the type described above, with length L metres. Treat the jumper as a particle so that the height of the person can be neglected.

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I really need help with this one, i have no clue where to start and how to do it, its really confusing.