Oscillations
The First Law of Thermodynamics & Oscillations
What is the First Law?
The First Law is a statement of energy conservation for thermodynamic systems: $$\Delta U = Q - W$$ where
- ΔU = change in internal energy
- Q = heat added to the system (positive if added)
- W = work done by the system (positive if the system does work)
Connecting to Oscillations
Oscillatory systems (springs, pendulums, LC circuits) exchange energy between two forms: kinetic and potential.
When no external heat or work is added, the total mechanical energy remains constant, mirroring the First Law with \(Q=W=0\).
🔄 Example: A mass on a spring oscillates, converting spring potential energy to kinetic energy and back, just like a pendulum swings back and forth.
Energy Flow in a Simple Spring Oscillator
| Time | Potential Energy (U) | Kinetic Energy (K) | Total Energy (E) |
|---|---|---|---|
| 0 | max | 0 | constant |
| T/4 | half | half | constant |
| T/2 | 0 | max | constant |
Real‑World Analogy
Imagine a playground swing.
- When you push (doing work), you add energy (Q).
- As the swing moves, that energy shifts between potential (height) and kinetic (speed).
- If you let go and no friction acts, the swing keeps oscillating forever – total energy stays the same.
Key Takeaways for A‑Level
- Write the First Law as \( \Delta U = Q - W \) and remember the sign conventions.
- For isolated oscillatory systems, \(Q=W=0\) → \( \Delta U = 0 \) → total mechanical energy is constant.
- Use energy conservation to solve for unknowns in simple harmonic motion problems.
- Always check units: joules for energy, watts for power, etc.
Quick Practice Question
A 0.5 kg mass is attached to a spring with \(k = 200\,\text{N/m}\).
It is displaced 0.1 m from equilibrium and released from rest.
What is the maximum kinetic energy of the mass during oscillation?
🧠 Hint: Use \(E_{\text{max}} = \frac{1}{2}kA^2\).
Answer: \(E_{\text{max}} = \frac{1}{2} \times 200 \times 0.1^2 = 1\,\text{J}\).
Revision
Log in to practice.