🤓 Basics

• SHM involves the transfer of energy between potential (Ep) and kinetic (Ek).

💡 Real-world Example: Imagine a swinging pendulum. At its highest point, it has maximum potential energy but zero kinetic energy. As it swings down, potential energy gets converted to kinetic energy.

🧮 Kinetic Energy (Ek)

• Formula: Ek=\(\frac 12\)​mv²
• For SHM: v² = ω²(x0² − x²) Thus, Ek=\(\frac 12\)​mω²(x0²−x²)

🧮 Potential Energy (Ep)

• Formula: Ep=Etot−Ek
• After a bit of math: Ep =\(\frac 12\)​mω²x²

🔍 Total Energy (Etot)

• When the object is moving the fastest (x=0),

Etot = \(\frac 12\)​mω²x0²

📊 Graphical Insights

• The graphs for Ek and Ep vs. displacement are shaped like parabolas.
• The point where Ek = Ep isn't at half the amplitude but closer to x0 (amplitude) from the equilibrium.

💡 Real-world Example: Think of a roller coaster. The potential energy is maximum at the top, and as it descends, kinetic energy increases. The shapes of these energy curves would be parabolic!

(Refer to the given graph for visual representation.)

• Amplitude of motion: 20 cm a. Total energy = 8.0 J b. When Ek = Ep - Displacement is approximately ±14 cm. c. Ek vs. displacement: Inverted parabolic shape compared to the Ep graph. d. Maximum speed = 2.5 m/s e. Oscillation period = 0.51 s