Law of Conservation of Energy

‘Energy can neither be created nor destroyed. It can be converted from one form into another. Thus, the total amount of energy in the universe remains constant.’

potential energy + kinetic energy = constant

`"mgh" + 1/2"mv"^2 = "constant"`

The sum of kinetic energy and potential energy of an object is its total mechanical energy.
We find that during the free fall of the object, the decrease in potential energy, at any point in its path, appears as an equal amount of increase in kinetic energy. (Here the effect of air resistance on the motion of the object has been ignored.) There is thus a continual transformation of gravitational potential energy into kinetic energy.

1. Aim: To demonstrate energy transfer between two coupled pendulums.

2. Requirements: Two nuts, thread, and horizontal support (such as a rod or stick).

3. Procedure

• Cut two equal lengths of thread and attach a nut to each thread, forming two pendulums of the same length.
• Tie another thread in a horizontal position to act as a support.
• Attach the pendulums to the horizontal thread, ensuring they hang freely and do not collide while swinging.
• Swing one pendulum and observe the motion of both pendulums over time.

Coupled Oscillators

4. Observation: Initially, only the first pendulum swings. Gradually, its oscillation slows down while the second pendulum, initially stationary, starts to swing. The first pendulum transfers its energy to the second pendulum through the horizontal thread.

5. Conclusion: This experiment demonstrates the concept of energy transfer in coupled oscillators. The motion of one pendulum induces motion in the other, highlighting how energy can be shared between systems connected by a common medium. This phenomenon is an example of mechanical resonance and coupling in oscillatory systems.