Understanding the Simple Harmonic Motion (SHM) of a Spring
* Potential Energy: When the mass is at its extreme positions (farthest from the equilibrium/mean position), all its energy is stored as potential energy. The spring is stretched or compressed to its maximum extent, and this stored energy is waiting to be released.
* Kinetic Energy: As the mass starts moving towards the mean position, the potential energy stored in the spring is converted into kinetic energy. The mass gains speed as it approaches the mean position.
* Conservation of Energy: The total mechanical energy of the system (potential + kinetic) remains constant. This means that as the mass moves towards the mean position, the potential energy decreases, and the kinetic energy increases.
Why Velocity is Maximum at the Mean Position
* Zero Potential Energy: At the mean position, the spring is neither stretched nor compressed. This means there's no potential energy stored in the spring.
* Maximum Kinetic Energy: Since all the potential energy has been converted into kinetic energy, the mass has its maximum velocity at the mean position.
Why Velocity is Zero at the Extreme Positions
* Maximum Potential Energy: At the extreme positions, all the energy is in the form of potential energy. The spring is either fully stretched or compressed, and the mass is momentarily stationary.
* Zero Kinetic Energy: Since there's no kinetic energy, the mass has zero velocity at the extreme positions.
Visualizing it
Imagine a swinging pendulum. At the highest points of its swing (extreme positions), it momentarily stops. This is similar to the mass attached to a spring. At the mean position, the pendulum has its maximum speed. This is analogous to the mass attached to a spring having its maximum velocity at the mean position.
Key Point: The velocity of the mass attached to the spring changes continuously as it oscillates between the mean and extreme positions. It's important to understand that the mass doesn't suddenly jump from zero velocity to maximum velocity. It's a gradual change, accelerating as it moves towards the mean position and decelerating as it moves towards the extreme positions.
