- #1

User1265

- 29

- 1

- Homework Statement
- I am confused how the time period of a vertical spring system is T= 2π√m/k, when there is the weight of the mass to consider?

- Relevant Equations
- T= = 2π *√m/k

I understand the derivation of T= 2π√m/k is a= -kx/m, in a mass spring system horizonatally on a smooth plane,

as this equated to the general equation of acceleration of simple harmonic motion , a= - 4π^2 (1/T^2) x

but surely when in a vertical system , taking downwards as -ve, ma = kx - mg , so I don't understand why in the following context of the question below

A bungee jumper of mass 70kg has a light linear elastic bungee cord with coefficient of elasticity 153N/m. He jumps from the platform and then bounces up and down at the end of the bungee cord. Assuming that the amplitude of bouncing is small enough that the bungee cord is never slack, what is the period of the steady state bouncing?

Why is T = 2π *√m/k is used to calculate the period, surely it can't have the same derivation as a horizontal spring-mass system as there is the constant force of gravity to consider?

My solution was intially to use:

Initially I used T = 2π *√m/k, but I had never really considered if I could get to the same derivation using a vertical spring system until now.

as this equated to the general equation of acceleration of simple harmonic motion , a= - 4π^2 (1/T^2) x

but surely when in a vertical system , taking downwards as -ve, ma = kx - mg , so I don't understand why in the following context of the question below

A bungee jumper of mass 70kg has a light linear elastic bungee cord with coefficient of elasticity 153N/m. He jumps from the platform and then bounces up and down at the end of the bungee cord. Assuming that the amplitude of bouncing is small enough that the bungee cord is never slack, what is the period of the steady state bouncing?

Why is T = 2π *√m/k is used to calculate the period, surely it can't have the same derivation as a horizontal spring-mass system as there is the constant force of gravity to consider?

My solution was intially to use:

Initially I used T = 2π *√m/k, but I had never really considered if I could get to the same derivation using a vertical spring system until now.