🔄 Oscillations (Chapter–13)
Complete Notes for Students
1. Periodic Motion
Motion that repeats itself after equal intervals of time.
Time Period (T): Time for one cycle
Frequency (f): Number of cycles per second
f = 1/T
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Frequency (f): Number of cycles per second
f = 1/T
2. Displacement as Function of Time
Periodic motion can be represented using sine or cosine functions.
x = A sin(ωt + φ)
- A = amplitude
- ω = angular frequency
- φ = phase constant
3. Simple Harmonic Motion (SHM)
Special type of periodic motion where restoring force is proportional to displacement.
F = −kx
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4. Equations of SHM
x = A sin(ωt)
v = ω√(A² − x²)
a = −ω²x
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v = ω√(A² − x²)
a = −ω²x
5. Phase
Phase describes the position and direction of motion at any instant.
---6. SHM and Uniform Circular Motion
Projection of uniform circular motion on a diameter gives SHM.
---7. Oscillation of Spring
F = −kx
T = 2π √(m/k)
T = 2π √(m/k)
- k = spring constant
- m = mass
8. Energy in SHM
Total Energy = ½ kA²
Kinetic Energy
KE = ½ m v²
Potential Energy
PE = ½ kx²
Total energy remains constant.
---9. Simple Pendulum
A simple pendulum performs SHM for small angles.
T = 2π √(L/g)
- L = length
- g = acceleration due to gravity
10. Important Points
- SHM is a type of periodic motion
- Restoring force always directed towards mean position
- Energy remains constant in SHM
- Time period independent of amplitude (for small oscillations)
