Discuss the meaning of the result for total energy in a whole mass spring system

In summary, the total energy in a whole mass spring system is the sum of potential and kinetic energy. It is calculated using the formula E = PE + KE, where PE is potential energy and KE is kinetic energy. A high total energy indicates a large amount of potential and kinetic energy in the system. The total energy changes as the system moves, with potential energy decreasing and kinetic energy increasing as the mass moves towards its equilibrium position. The significance of total energy lies in its role in determining the behavior of the system and the conservation of energy principle.
  • #1
hsut
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Homework Statement


Had to work out the total energy in a mass spring system (Part d of question), which has been found to be:

(v^2*m/4)[sin^2(nt) + sin^2(3nt)]


The next part of the question (e) says to 'Discuss the meaning of your result to part (d) above'

And I have no idea what to write! It is worth nearly 10% of the whole assignment! Any help would be much appreciated.

Thanks
 
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  • #2
Your expression for total energy depends on time periodically. This cannot be true. It must either monotonically decay with time (if friction/resistance is present), or be constant.
 

1. What is the total energy in a whole mass spring system?

The total energy in a whole mass spring system refers to the sum of the potential energy and kinetic energy of the system. It represents the amount of energy that is present in the system at any given time.

2. How is the total energy calculated in a mass spring system?

The total energy in a mass spring system can be calculated using the formula E = PE + KE, where E represents total energy, PE represents potential energy, and KE represents kinetic energy. Potential energy is calculated using the formula PE = 1/2kx^2, where k is the spring constant and x is the displacement of the mass from its equilibrium position. Kinetic energy is calculated using the formula KE = 1/2mv^2, where m is the mass of the object and v is its velocity.

3. What does a high total energy in a mass spring system indicate?

A high total energy in a mass spring system indicates that the system has a large amount of potential and kinetic energy. This could be due to a large displacement of the mass from its equilibrium position, a high spring constant, or a high velocity of the mass.

4. How does the total energy change in a mass spring system?

The total energy in a mass spring system can change as the system moves. As the mass moves towards its equilibrium position, potential energy decreases and kinetic energy increases. When the mass reaches its equilibrium position, potential energy is at its minimum and kinetic energy is at its maximum. As the mass moves away from its equilibrium position, the opposite effect occurs.

5. What is the significance of the total energy in a mass spring system?

The total energy in a mass spring system is significant because it determines the behavior of the system. A high total energy can lead to oscillations or harmonic motion, while a low total energy can result in a stable equilibrium. Additionally, the conservation of energy principle states that the total energy in a closed system remains constant, which is important in understanding the behavior of mass spring systems.

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