Oscillations & Simple Harmonic Motion (SHM)

Stage 1 – Page 9 | Time Period of SHM (Spring–Block & Pendulums)

1. Meaning of Time Period in SHM

Time Period (T) is the time taken by a particle to complete one full oscillation.

Time period depends on system parameters but never on amplitude (for ideal SHM).

2. Time Period of Spring–Block System

For a mass m attached to a spring of force constant k:

T = 2π √(m / k)

Independent of amplitude
Independent of gravity
Same for horizontal & vertical spring

IIT Insight:
Changing gravity does NOT affect spring time period.

3. Time Period of Simple Pendulum

For small angular oscillations:

T = 2π √(L / g)

L → length of pendulum
g → acceleration due to gravity

Valid only when angular displacement ≤ 10°.

4. Effect of Length & Gravity

T ∝ √L
T ∝ 1 / √g

If length increases → time period increases.

If gravity increases → time period decreases.

5. Effective Length of Pendulum

Effective length = distance between point of suspension and centre of bob.

Common Mistake:
Using string length instead of effective length.

6. Comparison: Spring vs Pendulum

Parameter	Spring–Block	Pendulum
Depends on mass	Yes	No
Depends on gravity	No	Yes
Depends on length	No	Yes
Depends on amplitude	No	No (small angle)

7. Time Period in Lift / Elevator

Lift accelerating upward → g increases → T decreases
Lift accelerating downward → g decreases → T increases
Free fall → g = 0 → T becomes infinite

High-Yield Topic:
Elevator problems are frequently asked in JEE.

8. Time Period on Different Planets

If gravity on planet is g':

T' = 2π √(L / g')

Lower gravity → longer time period.

9. Common IIT/JEE Traps

Using wrong length
Forgetting small angle condition
Assuming amplitude affects T
Wrong g in elevator problems

10. Why This Page Is Extremely Important

Direct formula questions
Ratio & comparison problems
Conceptual reasoning
Very high scoring

Stage 1 – Page 9 Completed Successfully ✅

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