Oscillations is an important chapter in Class 11 Physics that deals with repetitive motion of objects about a mean position. It forms the basis for understanding waves and many physical systems like pendulums and springs.
👉 Core Idea: Oscillatory motion is a periodic motion where a body moves to and fro about a fixed point.
1. Periodic and Oscillatory Motion
Periodic Motion
A motion that repeats itself after equal intervals of time.
Examples:
- Earth’s revolution
- Clock pendulum
Oscillatory Motion
Definition
A type of periodic motion in which a particle moves back and forth about a mean position.
Examples:
- Simple pendulum
- Mass attached to a spring
2. Displacement, Amplitude and Time Period
Displacement (x)
Distance of particle from mean position at any time.
Amplitude (A)
Maximum displacement from mean position.
Time Period (T)
Time taken to complete one oscillation.
Frequency (f)
f = 1/T
3. Simple Harmonic Motion (SHM)
Definition
An oscillatory motion in which restoring force is directly proportional to displacement and acts towards mean position.
Mathematical Form
F ∝ -x
F = -kx
Key Characteristics of SHM
- Motion is periodic
- Restoring force always towards mean position
- Acceleration proportional to displacement
4. Equation of SHM
Displacement
x = A sin(ωt + φ)
Where:
- A = amplitude
- ω = angular frequency
- φ = phase constant
Velocity
v = ω√(A² – x²)
Maximum velocity:
v_max = ωA
Acceleration
a = -ω²x
Maximum acceleration:
a_max = ω²A
5. Energy in SHM
Kinetic Energy
KE = (1/2)mω²(A² – x²)
Potential Energy
PE = (1/2)mω²x²
Total Energy
E = (1/2)mω²A²
👉 Concept Clarity:
Total energy remains constant.
6. Simple Pendulum
Definition
A small mass suspended by a light string that oscillates under gravity.
Time Period
T = 2π √(l/g)
Where:
- l = length of pendulum
- g = acceleration due to gravity
Important Points
- Independent of mass
- Depends on length and gravity
7. Spring Mass System
Time Period
T = 2π √(m/k)
Where:
- m = mass
- k = spring constant
8. Phase and Phase Difference
Phase
Describes the state of motion at any instant.
Phase Difference
Difference in phase between two oscillating particles.
9. Types of Oscillations
Free Oscillations
No external force acting
Damped Oscillations
Amplitude decreases over time
Forced Oscillations
External force applied
10. Resonance (Very Important)
Definition
Phenomenon in which amplitude becomes maximum when frequency of external force equals natural frequency.
Examples
- Swing
- Musical instruments
Important Numericals
Numerical 1
Find frequency if T = 2 s
f = 1/T = 1/2 = 0.5 Hz
Numerical 2
Find maximum velocity if A = 2 m, ω = 3 rad/s
v_max = ωA = 3 × 2 = 6 m/s
Numerical 3
Find time period of pendulum if l = 1 m, g = 9.8 m/s²
T = 2π √(1/9.8) ≈ 2 s
Numerical 4
Find total energy if m = 1 kg, ω = 2 rad/s, A = 0.5 m
E = (1/2)mω²A²
= 0.5 × 1 × 4 × 0.25 = 0.5 J
Important Formula Sheet
- x = A sin(ωt + φ)
- v = ω√(A² – x²)
- a = -ω²x
- T = 2π√(l/g)
- T = 2π√(m/k)
- E = (1/2)mω²A²
Concept Clarity (Important)
👉 WHY restoring force is negative?
Because it always acts towards mean position.
👉 WHY energy is constant in SHM?
Because there is no energy loss.
👉 WHY pendulum time period independent of mass?
Mass cancels in derivation.
Common Mistakes
- Confusing periodic and oscillatory motion
- Forgetting negative sign in SHM equation
- Using wrong formula for time period
Conclusion
Oscillations is a fundamental chapter that explains repetitive motion in physics. Understanding SHM, energy concepts, and pendulum motion is essential for mastering waves and higher topics.
👉 Focus on concept clarity + formulas + practice numericals.