# Energy and Damping In SHM

### Previously, the Velocity of a particle undergoing SHM was found by :- ### If this formula is combined with the Kinetic Energy formula, a method to find the Kinetic Energy of the particle at any given point in its motion can be derived :- ### As this is being modelled as an ideal system with no Energy loss :- ### Therefore at the equilibrium point of the oscillation, Etot = Ek + 0 it can be shown that :- ### By substituting into the general equation above, the Potential Energy can be shown by :- ### The graph below shows how the Ek and Ep vary across the entire oscillation :- ## Example 1 -

### The following graph shown the Potential Energy of a particle with mass = 0.4 kg undergoing SHM ### Ep = Ek ## Under-Damped System

### The graph below shows the motion of an under-damped object undergoing SHM :- ## Over Damped System

### The graph below shows the motion of an over-damped object undergoing SHM :- ## Critically Damped System

### The graph below shows the motion of a critically damped object undergoing SHM :- 