• Simple Harmonic Motion (SHM): An oscillatory motion where the restoring force is directly proportional and in the opposite direction to the displacement from its equilibrium position.
• Energy in SHM: Energy constantly shifts between kinetic energy (motion) and potential energy (stored).

🎈 Imagine a swinging pendulum on a grandfather clock. As the pendulum swings left and right, its energy keeps changing between being at rest (stored energy) and in motion (moving energy).

• At the extremes (furthest points of the swing):

  • Speed = 0
  • Kinetic Energy (motion energy) = 0
  • All energy is stored as Potential Energy.

• At the centre (middle point of the swing):

  • Speed is maximum
  • Kinetic Energy is maximum
  • Potential Energy (stored energy) = 0

🚗 Imagine a car on a springy track: When pushed and released, the car zips to the center of the track super-fast (lots of motion energy). But at the track's ends, it stops for a brief moment (all stored energy) before racing back again!

Did You Know? During one full swing (or cycle) of the pendulum

• Kinetic Energy peaks twice (once in each direction).
• Potential Energy peaks twice too.
• The number of energy transfers is DOUBLE the number of swings.

🎡 Imagine a Ferris wheel: If you're on a cabin, every time you're at the top (or bottom), that's like the pendulum reaching an extreme. The number of times you feel the "slowest" on the Ferris wheel (top and bottom) is double the number of full rounds you make!

• Example 1: If a body oscillates 20 times a second (20Hz), its kinetic energy is zero 40 times (2x20) in that second. Why? Because for each oscillation, the energy hits zero twice.
• Example 2: If the potential energy graph of a pendulum shows:
  • It hits zero at 0.2s (that's when it’s in the middle)
  • It’s half of the max at 0.1s (that's when kinetic and potential energies are equal)

Then, it takes 0.4s for half a swing. So, a full swing back and forth (complete oscillation) is 0.8s!