📚 IIT–JEE Physics Complete Learning Hub
🔹 Core Physics Libraries
- 🔁 Simple Harmonic Motion (SHM) – Complete Library (IIT–JEE Advanced)
- 🌊 Mechanical Waves – JEE Advanced Objective Library
- 🧠 IIT–JEE Physics Complete Master Library
🔹 Central Learning Platforms
📌 Structured • Exam-Oriented • IIT–JEE Advanced Focused Learning
Stage–2 | Page–6
Time Period, Amplitude Change & Energy Injection in SHM
Where most students lose marks — and toppers gain them
Time Period in SHM (Reinforced)
Time period depends only on system parameters — not on amplitude or energy.
Spring–Mass System: T = 2π √(m / k)
Simple Pendulum (small oscillations): T = 2π √(ℓ / g)
Simple Pendulum (small oscillations): T = 2π √(ℓ / g)
- Independent of amplitude
- Independent of energy
- Depends only on restoring force parameters
IIT Trap #1 – Amplitude Change ≠ Time Period Change
Changing amplitude changes energy, not time period.
Many students incorrectly modify time period when amplitude is changed.
Energy Injection in SHM
Energy injection means giving extra energy to the oscillator (by hit, push, collision, sudden release).
New Energy ∝ (New Amplitude)²
- Amplitude changes
- Frequency remains same
- Motion remains SHM
How Amplitude Changes
If Energy becomes n times → Amplitude becomes √n times
- Energy doubles → Amplitude increases by √2
- Energy becomes 4 times → Amplitude doubles
Sudden Stop / Sudden Release Cases
Very common in JEE Advanced.
- Block suddenly stopped → kinetic energy converts to PE
- String cut suddenly → new equilibrium shifts
- Mass added suddenly → amplitude changes
Golden Rule:
During sudden change, position does not change instantly.
During sudden change, position does not change instantly.
Sudden Change in Mass
If mass is suddenly changed:
- Equilibrium position shifts
- New SHM starts about new mean
- Amplitude must be calculated from geometry + energy
Time Period After Sudden Change
New T depends on new system parameters only
- Amplitude irrelevant
- Energy irrelevant
- Only m, k, ℓ, g matter
IIT Trap #2 – Mixing Energy with Phase
- Energy tells amplitude
- Phase tells position & velocity direction
- Never mix them blindly
How IIT Toppers Solve These Problems
- Step 1: Identify sudden vs gradual change
- Step 2: Fix old equilibrium
- Step 3: Find new equilibrium
- Step 4: Use energy to get new amplitude
- Step 5: Use formula only at the end
Next: Stage–2 Page–7
- Phase, initial conditions & phase constant
- Writing equation of SHM directly
- High-accuracy JEE problems
Stage–2 Page–6 Completed ✔ You now dominate amplitude & energy questions 🔥
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