NEB Class 12 Physics Periodic Motion Notes in PDF Complete Handwritten. Physics Notes 2081: All Chapters | New Curriculum | Class 12 Physics Notes download.
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NEB Class 12 Physics Periodic Motion Note Handwritten in PDF
What is Periodic Motion and SHM?
Periodic motion is any motion that repeats itself at equal time intervals. A clock pendulum, a vibrating guitar string, Earth’s rotation β all are periodic. Simple Harmonic Motion (SHM) is the most fundamental type of periodic motion.
SHM is defined as: Motion in which the restoring force is directly proportional to displacement and always directed toward the equilibrium position.
- Mathematical form: F = βkx or equivalently a = βΟΒ²x
- The negative sign is critical β force opposes displacement
- The graph of acceleration vs displacement is a straight line through origin with negative slope
Equation of SHM
The displacement of a particle performing SHM at any time t is:
x = A sin(Οt + Ο)
Where:
- A = amplitude (maximum displacement from equilibrium)
- Ο = angular frequency = 2Οf = 2Ο/T
- Ο = initial phase (depends on starting condition)
From this, velocity and acceleration can be derived:
- v = AΟ cos(Οt + Ο) = Οβ(AΒ² β xΒ²)
- a = βAΟΒ² sin(Οt + Ο) = βΟΒ²x
Key values to remember:
- Velocity is maximum (v = ΟA) at equilibrium (x = 0)
- Velocity is zero at extreme positions (x = Β±A)
- Acceleration is maximum (a = ΟΒ²A) at extremes
- Acceleration is zero at equilibrium
Energy in SHM
Energy in SHM constantly shifts between kinetic and potential forms, but total energy is always conserved.
- Kinetic energy: KE = Β½mΟΒ²(AΒ² β xΒ²)
- Potential energy: PE = Β½mΟΒ²xΒ²
- Total energy: E = KE + PE = Β½mΟΒ²AΒ² = Β½kAΒ²
Important observations:
- Total energy depends on amplitude squared β doubling amplitude quadruples energy
- At x = 0: KE = maximum, PE = 0
- At x = Β±A: KE = 0, PE = maximum
- At x = A/β2: KE = PE = E/2 (equal energy point)
Spring-Mass System
A mass m attached to a spring of constant k performs SHM when displaced.
Time period: T = 2Οβ(m/k)
Key points:
- Period is independent of amplitude β this is a defining property of SHM
- Heavier mass β longer period (more inertia)
- Stiffer spring (higher k) β shorter period (stronger restoring force)
- This derivation is a must-know 4-mark NEB question
Simple Pendulum
A simple pendulum (mass m, string length L, small angle) also performs SHM.
Time period: T = 2Οβ(L/g)
Key points:
- Valid only for small angles (less than ~15Β°)
- Period depends on length and g, but not on mass or amplitude (for small angles)
- Longer pendulum β longer period
- At higher altitude (g decreases) β period increases β clock runs slow
- This is one of the most commonly asked derivations in NEB exams
Damped Oscillation
In real life, all oscillations lose energy due to friction and air resistance β this is called damping.
Three types of damping:
- Underdamped: Oscillations continue but amplitude decreases gradually (spring in air)
- Critically damped: System returns to equilibrium as fast as possible without oscillating (car suspension)
- Overdamped: System returns slowly without oscillating (door closer mechanism)
Forced Oscillation and Resonance
When an external periodic force is applied to a system:
- Forced oscillation: System vibrates at the frequency of the external force
- Resonance: Occurs when driving frequency = natural frequency of system β amplitude becomes maximum
Examples of resonance:
- Pushing a child on a swing at the right rhythm (useful)
- Tacoma Narrows Bridge collapse β wind resonated with bridge’s natural frequency (destructive)
- MRI machines use resonance of hydrogen nuclei
- Radio/TV tuning circuits use electrical resonance
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Frequently Asked Questions
What is simple harmonic motion in Class 12 Physics?
Physics? SHM is periodic motion where restoring force is proportional to displacement and directed toward equilibrium. Equation: a = βΟΒ²x. Examples include mass on spring, simple pendulum for small angles, and vibrating tuning fork. It is the most fundamental periodic motion studied in NEB Class 12 Physics.
What is the time period formula for simple pendulum Class 12?
Time period of simple pendulum: T = 2Οβ(L/g). Valid only for small angles below 15Β°. Period is independent of mass and amplitude β a key property of SHM. This derivation is asked almost every year in NEB board exam as a 4-mark long answer question.
What is the difference between damped and forced oscillation?
Damped oscillation loses energy to friction β amplitude decreases gradually with no external force. Forced oscillation is driven by an external periodic force maintaining the motion. When driving frequency matches natural frequency, resonance occurs and amplitude becomes maximum. Resonance can be useful or destructive depending on the situation.
What is energy in SHM Class 12 Physics?
Total energy in SHM = Β½mΟΒ²AΒ² = constant. KE = Β½mΟΒ²(AΒ²βxΒ²) is maximum at equilibrium where x=0. PE = Β½mΟΒ²xΒ² is maximum at extremes where x=Β±A. At x = A/β2, KE equals PE exactly. Total mechanical energy is always conserved throughout the entire SHM motion.
What is the time period of spring mass system NEB Class 12?
Time period of spring-mass system: T = 2Οβ(m/k). Heavier mass gives longer period. Stiffer spring (higher k) gives shorter period. Period is completely independent of amplitude this is a defining property of SHM. This formula and its derivation is a regular NEB board exam question.
What is resonance in Class 12 Physics with example?
Resonance occurs when driving frequency equals natural frequency β amplitude becomes maximum. Examples: Tacoma bridge collapse in 1940 (wind matched bridge’s natural frequency), radio tuning (adjust capacitance to match station frequency), MRI machines, and microwave ovens heating water molecules at their natural frequency.
What is the difference between free and forced oscillation?
Free oscillation occurs at the system’s own natural frequency with no external force β amplitude stays constant without damping. Forced oscillation is driven by external periodic force at a different frequency. The system responds at the driving frequency rather than its own natural frequency.
Which SHM topics are most important for NEB 2082 exam?
Most important: simple pendulum T derivation, spring-mass T derivation, energy expressions in SHM, velocity at displacement v=Οβ(AΒ²βxΒ²), and resonance explanation with example. Numericals on finding time period, energy, and velocity at a given displacement appear regularly in NEB board papers.
