Introduction to Simple Harmonic Motion

Simple Harmonic Motion (SHM) is a fundamental chapter in NEET Physics that explains periodic oscillatory motion where the restoring force is directly proportional to the displacement and acts in the opposite direction.

Understanding SHM is vital for NEET aspirants as it forms the basis of pendulum motion, spring oscillations, and waves.

StudentBro notes provide conceptual clarity, derivations, and solved examples to help students master this chapter for NEET exams.

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Definition and Conditions for SHM

• Definition: Motion of a body is called SHM if its acceleration is directly proportional to displacement from equilibrium and directed towards equilibrium.

• Mathematical condition: a = −ω²x

  • a = acceleration

  • x = displacement from mean position

  • ω = angular frequency

• NEET questions may ask to identify whether a given motion is simple harmonic or not.

Displacement, Velocity, and Acceleration in SHM

• Displacement (x): Distance from equilibrium at any instant.

• Velocity (v): v = dx/dt = ±ω√(A² − x²)

  • Maximum at equilibrium, zero at extreme positions

• Acceleration (a): a = −ω²x

  • Maximum at extreme positions, zero at equilibrium

• Phase: Phase angle determines position and motion at a particular time

• NEET questions often involve graphical interpretation of displacement, velocity, and acceleration.

Time Period and Frequency

• Time Period (T): Time for one complete oscillation

• Frequency (f): Number of oscillations per second, f = 1/T

• For a mass-spring system: T = 2π√(m/k)

• For a simple pendulum: T = 2π√(l/g)

• NEET numericals may involve calculating T and f for different systems.

Amplitude and Phase

• Amplitude (A): Maximum displacement from equilibrium

• Phase (φ): Determines instantaneous position in oscillation

• NEET conceptual questions may include relation between phase, displacement, and velocity.

Energy in SHM

• Total mechanical energy (E): Sum of kinetic and potential energy, E = ½ k A²

• Kinetic energy (KE): KE = ½ k (A² − x²)

• Potential energy (PE): PE = ½ k x²

• Energy oscillates between kinetic and potential forms, total energy remains constant

• NEET problems often involve calculating energy at different displacements.

Examples of SHM

1. Mass-spring system: Spring with force constant k and mass m

2. Simple pendulum: Mass suspended on a string of length l

3. Oscillations of liquid in a U-tube

4. Torsional pendulum

StudentBro notes provide stepwise derivations of time period and energy for these examples.

Relation Between SHM and Circular Motion

• SHM can be viewed as projection of uniform circular motion on a diameter

• Displacement: x = A cos(ωt + φ)

• Velocity: v = −ω A sin(ωt + φ)

• Acceleration: a = −ω² A cos(ωt + φ)

• NEET questions often include conceptual understanding of SHM from circular motion.

Damping and Resonance

• Damped SHM: Amplitude decreases over time due to resistive forces

• Resonance: When frequency of external force matches natural frequency, amplitude is maximum

• Conceptual NEET questions may ask for effects of damping and resonance in oscillatory systems.

Graphical Representation

• Displacement vs time (x–t): Sinusoidal

• Velocity vs time (v–t): 90° phase difference with displacement

• Acceleration vs time (a–t): 180° out of phase with displacement

• NEET numericals and reasoning questions often involve interpreting these graphs.

Applications for NEET

• Calculating time period and frequency of pendulums and springs

• Determining displacement, velocity, and acceleration at a given time

• Energy calculations in SHM

• Understanding resonance and damping in mechanical and practical systems

• Interpreting graphs of displacement, velocity, and acceleration

StudentBro notes include real-life examples and solved problems for better exam readiness.

Tips for NEET Preparation on SHM

1. Memorize formulas for time period, frequency, velocity, and acceleration

2. Understand phase relationships between displacement, velocity, and acceleration

3. Practice energy-related numericals for mass-spring and pendulum systems

4. Visualize SHM as projection of circular motion

5. Solve graph-based problems for displacement, velocity, and acceleration curves

Advantages of StudentBro NEET Physics Notes

• Covers displacement, velocity, acceleration, energy, time period, frequency, and examples of SHM

• Step-by-step derivations, solved numericals, and diagrams included

• Structured for easy revision and conceptual clarity

• Focused on NEET syllabus and high-yield problems

These notes ensure aspirants can confidently tackle SHM questions in NEET exams.

Conclusion

The chapter Simple Harmonic Motion is an essential part of NEET Physics under mechanics and oscillations. Mastery of displacement, velocity, acceleration, energy, time period, and phase relationships is crucial for solving both conceptual and numerical problems.

StudentBro NEET Physics notes provide structured, clear, and exam-focused guidance, enabling aspirants to confidently solve SHM questions and excel in NEET exams.