# Derive the kinetic energy of a mass on two springs

I doing right for calculating the kinetic energy for the mass on two springs ?In summary, the conversation discusses deriving the equation of kinetic energy for a mass on two springs using the formula ΔK = ∫ F(x) · dx. The person asks for clarification on the limits of the integral and the response suggests starting at a point where KE = 0 to determine the actual KE at a given point.

## Homework Statement

Hi

I want to derive the equation of kinetic energy for a mass on two springs .. Here is the figure of the system:
http://faculty.ndhu.edu.tw/~clcheng/class-98/gen-phy98/gen-phy98-1-Q2s.pdf

Am I doing right for calculating the kinetic energy for the mass on two springs ?

ΔK = ∫ F(x) · dx

## The Attempt at a Solution

My attempt to solve the kinetic equation is by using this formula :

ΔK = ∫ F(x) · dx

so ΔK = (-2kx^2)/2 + ∫ 2kxL/(√(x^2 + L^2)) = (-2kx^2)/2 + 2kL*√(x^2 + L^2)

Am I doing right for calculating the kinetic energy for the mass on two springs ?

Thanks

What are the limits for your integral?

You have to integrate between, say, x0 and x. To determine the actual KE at a given point you would need to start at the value for x0 where KE = 0.

AM

## What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion.

## How is kinetic energy calculated?

Kinetic energy is calculated by multiplying the mass of an object by its velocity squared.

## What are the two types of kinetic energy?

The two types of kinetic energy are translational kinetic energy, which is associated with the overall motion of an object, and rotational kinetic energy, which is associated with the spinning or rotating motion of an object.

## What are the units of kinetic energy?

The units of kinetic energy are Joules (J) in the International System of Units (SI) and foot-pounds (ft·lb) in the imperial system.

## How do springs contribute to kinetic energy?

When a mass is attached to two springs, the springs store potential energy as they stretch or compress. When the mass is set in motion, the potential energy is converted into kinetic energy, contributing to the total kinetic energy of the system.