To calculate the energy in a mass-spring system that moves in a Simple Harmonic Motion (SHM), we look at two types of energy: kinetic energy (KE) and potential energy (PE).

The total energy (E) in a perfect mass-spring system stays the same and can be written like this:

E = KE + PE

Let’s break it down:

1. Kinetic Energy (KE): Kinetic energy is the energy of the mass when it is moving. You can calculate it using this formula:

   KE = 1/2 mv²

   Here:

   • ( m ) is the mass in kilograms (kg).
   • ( v ) is the speed in meters per second (m/s).

2. Potential Energy (PE): Potential energy is the energy stored in the spring. It can be calculated using this formula:

   PE = 1/2 kx²

   In this formula:

   • ( k ) is the spring constant measured in Newtons per meter (N/m).
   • ( x ) is how far the spring is stretched or compressed from its resting position in meters (m).

3. Total Mechanical Energy: In a mass-spring system, energy moves between KE and PE, but the total energy remains the same. This can be shown as:

   E = 1/2 k A²

   Here:

   • ( A ) is the amplitude, which is the maximum distance the spring moves from its resting position in meters (m).

This information shows how mass and the spring constant affect the energy in the system.