Spring mass system with applied force kinetic energy

In summary, the conversation is about using Lagrangian mechanics to model a spring mass system with a force acting at the center of mass. The person is having trouble calculating the kinetic energy and is considering using the equation ΔKE + ΔPE = W. They also mention using Lagrangian mechanics for double spring systems with applied force.
  • #1
fobos3
34
1
I'm trying to work out a model for a spring mass system with a force acting at the centre of mass of the mass using Lagrangian mechanics. I can't work out the kinetic energy. I know the kinetic energy [tex]\text{KE}=\dfrac{1}{2}mv^2[/tex]. I also have [tex]W=\int_a^b F \, dt[/tex].
Should I use [tex]\Delta \text{KE} + \Delta \text{PE} =W[/tex]

Some help will be appreciated.

P.S. I'm using Lagrangian mechanics because later I'm planning some calculations on double spring systems with applied force.
 
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  • #2
W = [tex]\int[/tex] [tex]\vec{F}[/tex] [tex]\cdot[/tex] [tex]\vec{dx}[/tex]

The expression you had was for Impulse not Work
 
  • #3


Hello,

It seems like you are on the right track with using Lagrangian mechanics to model your spring mass system with an applied force. In order to calculate the kinetic energy for this system, you will need to consider the motion of the mass in response to the applied force. This means taking into account both the translational and rotational motion of the mass.

To do this, you can use the formula for kinetic energy that you mentioned, \text{KE}=\dfrac{1}{2}mv^2, but you will need to consider the velocities in both the x and y directions. You can also use the formula for rotational kinetic energy, \text{KE}=\dfrac{1}{2}I\omega^2, where I is the moment of inertia and \omega is the angular velocity.

Additionally, you will need to consider the work done by the applied force in order to incorporate it into the kinetic energy calculation. This is where the formula \Delta \text{KE} + \Delta \text{PE} =W can be useful. It states that the change in kinetic energy plus the change in potential energy (due to the applied force) is equal to the work done by the force. By rearranging this equation, you can solve for the kinetic energy.

I hope this helps and good luck with your calculations on double spring systems!
 

1. What is a spring mass system with applied force?

A spring mass system with applied force is a physical system that consists of a mass attached to a spring, with an external force applied to the mass. The system is often used to model simple harmonic motion.

2. How is kinetic energy related to a spring mass system with applied force?

Kinetic energy in a spring mass system with applied force is the energy that the mass possesses due to its motion. It is related to the displacement of the mass from its equilibrium position and the spring constant of the system.

3. What factors affect the kinetic energy in a spring mass system with applied force?

The factors that affect the kinetic energy in a spring mass system with applied force include the mass of the object, the amplitude of the oscillations, and the frequency of the oscillations. The spring constant and the applied force also play a role in determining the kinetic energy.

4. How does the kinetic energy change over time in a spring mass system with applied force?

The kinetic energy in a spring mass system with applied force varies sinusoidally over time. It reaches its maximum value when the mass is at its maximum displacement from equilibrium and decreases to zero when the mass passes through its equilibrium position.

5. Can the kinetic energy in a spring mass system with applied force be converted into other forms of energy?

Yes, the kinetic energy in a spring mass system with applied force can be converted into other forms of energy, such as potential energy. When the mass is at its maximum displacement, it has maximum potential energy, and when it is at its equilibrium position, it has zero potential energy.

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