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## Differential Equations Bungee Jumping question

The general solution of harmonic oscillator equation is a combination of $sin omega t$ and $cos omega t$ where $omega = sqrt $. Since $x(0)=0$, we only have the sine. So, $x(t)=Asinomega t$. To find $A$, you can use the relation $x'(0)=Aomega$, where $x'(0)$ can be found from energy consideration. Indeed, jumping from height $x=-h$, the person acquires kinetic energy $mgh $ by the time that $x=0$. Hence, $x'(0)=sqrt$.

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### Becky

Updated on August 01, 2022

### Comments

So I was given a problem about bungee jumping,and it’s obviously important to know in advance how far the cord of unstretched length L will stretch for a given weight of person. Consider the cord to be a weak spring with constant k and the person is a point mass m. Air resistance and pendulum motion are ignored. Point x=0 would be the point where the person freely fell until the entire slack of the cord is extended to length L. After the person passes x=0, the cord is stretched x(t).

Simple enough right? Well I was having trouble:

find a model for x(t) defined only on the first interval of time 0=0. Solve for x(t) and then determine maximum elongation. I do know that I should use x(t)=A sin(ωt+ φ) but after than I’m stuck. Could anyone possibly help me?

Maybe the *The Physics Of Bungee Jumping* will help? See equation 13 and the substitution they make for **a**. Regards

## Differential Equations Bungee Jumping question

The general solution of harmonic oscillator equation is a combination of $sin omega t$ and $cos omega t$ where $omega = sqrt $. Since $x(0)=0$, we only have the sine. So, $x(t)=Asinomega t$. To find $A$, you can use the relation $x'(0)=Aomega$, where $x'(0)$ can be found from energy consideration. Indeed, jumping from height $x=-h$, the person acquires kinetic energy $mgh $ by the time that $x=0$. Hence, $x'(0)=sqrt$.

#### Related videos on Youtube

### Becky

Updated on August 01, 2022

### Comments

So I was given a problem about bungee jumping,and it’s obviously important to know in advance how far the cord of unstretched length L will stretch for a given weight of person. Consider the cord to be a weak spring with constant k and the person is a point mass m. Air resistance and pendulum motion are ignored. Point x=0 would be the point where the person freely fell until the entire slack of the cord is extended to length L. After the person passes x=0, the cord is stretched x(t).

Simple enough right? Well I was having trouble:

find a model for x(t) defined only on the first interval of time 0=0. Solve for x(t) and then determine maximum elongation. I do know that I should use x(t)=A sin(ωt+ φ) but after than I’m stuck. Could anyone possibly help me?

Maybe the *The Physics Of Bungee Jumping* will help? See equation 13 and the substitution they make for **a**. Regards

## Differential Equations Bungee Jumping question

The general solution of harmonic oscillator equation is a combination of $sin omega t$ and $cos omega t$ where $omega = sqrt $. Since $x(0)=0$, we only have the sine. So, $x(t)=Asinomega t$. To find $A$, you can use the relation $x'(0)=Aomega$, where $x'(0)$ can be found from energy consideration. Indeed, jumping from height $x=-h$, the person acquires kinetic energy $mgh $ by the time that $x=0$. Hence, $x'(0)=sqrt$.

#### Related videos on Youtube

### Becky

Updated on August 01, 2022

### Comments

So I was given a problem about bungee jumping,and it’s obviously important to know in advance how far the cord of unstretched length L will stretch for a given weight of person. Consider the cord to be a weak spring with constant k and the person is a point mass m. Air resistance and pendulum motion are ignored. Point x=0 would be the point where the person freely fell until the entire slack of the cord is extended to length L. After the person passes x=0, the cord is stretched x(t).

Simple enough right? Well I was having trouble:

find a model for x(t) defined only on the first interval of time 0=0. Solve for x(t) and then determine maximum elongation. I do know that I should use x(t)=A sin(ωt+ φ) but after than I’m stuck. Could anyone possibly help me?

Maybe the *The Physics Of Bungee Jumping* will help? See equation 13 and the substitution they make for **a**. Regards

Source https://9to5science.com/differential-equations-bungee-jumping-question

Source https://9to5science.com/differential-equations-bungee-jumping-question

Source https://9to5science.com/differential-equations-bungee-jumping-question