Subsection 3.2.1 Principle of Conservation of Energy
It states that in an isolated system, the total energy of the system is conserved. Meaning, energy can neither be created nor be destroyed, it can only be converted from one form of energy to another. For example, when a stone falls from a roof its potential energy is converted into kinetic energy just before it hits the ground. When friction slows down the block to a stop, the kinetic energy is converted into thermal energy. In case of mechanical energy, the sum of kinetic energy and potential energy is conserved. That is, total energy at any moment of time
\begin{equation}
E_i =E_f\tag{3.2.1}
\end{equation}
is always same. Mechanical energy is due to the position and motion of the object. Therefore,
\begin{equation}
E = KE + PE = \frac{1}{2}mv^2 + mgh\tag{3.2.2}
\end{equation}
In simple pendulum, when the bob is left from a displaced position it starts swinging to and fro motion due to conservation of energy. As its potential energy (PE) is converted into kinetic energy (KE) at the mean position acquire maximum velocity and keep moving otherside of mean position due to inertia. Once it reaches to another extrema it falls back again and retraces it path again and again. Click this link simple pendulum and try to understand conservation of energy principle. During the motion of a swinging pendulum, the energy is constantly changing from KE (kinetic energy) to PE (potential energy).
1
www.mathsisfun.com/physics/pendulum.html- KE is MAX at lowest point,
- KE is MIN at the top of the path (\(v = 0\)),
- PE is MAX at top of path.
