# Oscillation and height

• abeltyukov
This gives you the potential energy at the start.In summary, Jose, with a mass of 90 kg, has completed his first bungee jump with an initial amplitude of 9 m and a period of 4.0 s. The spring constant of the bungee cord is 222.0661 N/m and his maximum speed is 14.137167 m/s. With a damping constant of 6.0 kg/s, Jose will make 16.479 oscillations before his amplitude decreases to 1.0 m. To calculate the height from which Jose jumped, the kinetic energy from his fall can be divided into potential energy to stretch the bungee and any remaining kinetic energy. This can be calculated at

## Homework Statement

Jose, whose mass is 90 kg, has just completed his first bungee jump and is now bouncing up and down at the end of the cord. His oscillations have an initial amplitude of 9 m and a period of 4.0 s.

2. The attempt at a solution

a) The spring constant of the bungee cord is 222.0661 N/m

b) The maximum speed at which Jose is oscillating is 14.137167 m/s

c) If the damping constant due to air resistance is 6.0 kg/s, the number of oscillations which Jose makes before his amplitude has decreased to 1.0 m is 16.479

d) From what height above the lowest point did Jose jump? (in meters)

I got every other part of the question right but am having trouble figuring out part d. Do I use F=ma? Any help would be appreciated.

Thanks!

The kinetic energy from Jose's fall went into two places. The first is the potential energy to stretch the bungee to a new equilibrium position (the center of his oscillations). You can get that from his weight and the spring constant. The second is any kinetic energy when he is moving. You can calculate the sum of the these at any convenient point in his oscillation - maybe easiest to do it at the top or bottom where the kinetic energy vanishes.