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Science Class 11 - Oscillations Notes

Comprehensive study notes for Class 11 - Oscillations olympiad preparation

Oscillations

Welcome to the chapter on Oscillations for Class 11. In this chapter, you will learn about periodic motion, simple harmonic motion (SHM), the mathematics of oscillations, energy in oscillatory systems, and real-life examples of oscillations. By the end of this chapter, you will be able to describe, analyze, and solve problems related to oscillatory motion.

Key Concepts

  • Oscillation: Repeated to-and-fro motion about a mean position.
  • Periodic Motion: Motion that repeats itself at regular intervals.
  • Simple Harmonic Motion (SHM): A special type of periodic motion where the restoring force is directly proportional to displacement and acts towards the mean position.

Simple Harmonic Motion (SHM)

SHM is defined by the equation:

F = -kx

  • F: Restoring force
  • k: Force constant
  • x: Displacement from mean position

The general solution for displacement in SHM is:

x(t) = A sin(ωt + φ)

  • A: Amplitude (maximum displacement)
  • ω: Angular frequency (ω = 2π/T)
  • T: Time period
  • φ: Phase constant

Time Period and Frequency

  • Time Period (T): Time taken for one complete oscillation.
  • Frequency (f): Number of oscillations per second (f = 1/T).

Energy in SHM

  • Kinetic Energy (KE): KE = (1/2)mω²(A² - x²)
  • Potential Energy (PE): PE = (1/2)mω²x²
  • Total Energy (E): E = (1/2)mω²A² (constant for SHM)

Examples of Oscillatory Motion

  • Simple pendulum
  • Mass-spring system
  • Vibrating tuning fork
  • Oscillations of molecules in solids

Damped and Forced Oscillations

  • Damped Oscillation: Amplitude decreases over time due to energy loss (e.g., friction).
  • Forced Oscillation: An external periodic force is applied to keep the oscillation going.
  • Resonance: When the frequency of the external force matches the natural frequency, amplitude becomes maximum.

Practice Questions

  1. Write the equation for SHM and explain each term.
  2. A mass of 0.5 kg attached to a spring has a force constant of 200 N/m. Find the time period of oscillation.
  3. What is the total energy of a particle of mass 0.2 kg performing SHM with amplitude 0.1 m and angular frequency 5 rad/s?
  4. Explain the difference between damped and forced oscillations.
  5. What is resonance? Give an example from daily life.

Challenge Yourself

  • Derive the expression for the time period of a simple pendulum.
  • Show that the total energy in SHM remains constant.
  • Explain why resonance can be dangerous in bridges and buildings.

Did You Know?

  • The motion of a swing is an example of oscillation.
  • Musical instruments like guitars and drums use oscillations to produce sound.

Glossary

  • Oscillation: Repeated back-and-forth motion about a mean position.
  • Amplitude: Maximum displacement from the mean position.
  • Frequency: Number of oscillations per second.
  • Resonance: Large amplitude oscillation when external frequency matches natural frequency.

Answers to Practice Questions

  1. x(t) = A sin(ωt + φ), where A is amplitude, ω is angular frequency, t is time, and φ is phase constant.
  2. T = 2π√(m/k) = 2π√(0.5/200) ≈ 0.314 s
  3. E = (1/2)mω²A² = 0.5 × 0.2 × 25 × 0.01 = 0.025 J
  4. Damped oscillations lose energy over time; forced oscillations are maintained by an external force.
  5. Resonance is when the driving frequency matches the natural frequency, causing large amplitude (e.g., a singer breaking a glass by singing at its natural frequency).

Understanding oscillations helps you explore the world of waves, sound, and vibrations in physics!

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