📚 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 3 – Page 6
Simple Harmonic Motion (SHM) – Non-Standard Systems & Constraints
1. What is a Non-Standard SHM?
Any system that does NOT look like a simple spring–mass but still follows:
Restoring Force ∝ Displacement
Key skill: Convert the system into SHM mathematically
2. Effective Restoring Force Concept
If net force can be written as:
F = −keff x
Then motion is SHM with:
ω = √(keff / m)
3. SHM on Inclined Plane (Spring Attached)
- Inclination shifts equilibrium position
- Does NOT affect time period
T = 2π√(m/k)
Gravity changes mean position, not oscillation nature
4. SHM of Block in a Smooth Circular Track
For small angular displacement (θ):
Restoring force ≈ mgθ
Angular SHM:
ω = √(g/R)
Small angle approximation is the key
5. SHM of Floating Object
For a floating body displaced vertically:
- Restoring force comes from buoyancy change
keff = ρgA
ω = √(ρgA / m)
Frequently asked in JEE Advanced
6. SHM with Pulley Constraints
When pulleys are involved:
- Displacement relation reduces degrees of freedom
- Effective mass changes
Always express motion using a single coordinate
7. SHM in Variable Force Fields
If force varies with position:
F(x) ≈ −(d²U/dx²)eq x
Then:
keff = d²U/dx² at equilibrium
8. Small Oscillation Technique (Advanced)
Steps:
- Find equilibrium position
- Displace slightly
- Linearize force or torque
- Extract keff
This method converts complex problems into SHM
9. Common IIT Traps
- Ignoring constraint relations
- Using wrong equilibrium reference
- Missing effective mass change
Stage 3 – Page 6 Key Takeaways
✔ SHM is hidden in many systems
✔ Linearization near equilibrium is essential
✔ Effective k decides everything
— Stage 3 | SHM Deep Systems —
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