Class XII Physics: Oscillations Overview

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the formula for the force acting on a simple pendulum?

  • F = mg cos 
  • F = mg sin  (correct)
  • F = mg tan 
  • F = mg cot 

What happens to the time period of a simple pendulum when the angle of displacement is very small?

  • The time period increases.
  • The time period decreases.
  • The time period remains constant. (correct)
  • The time period becomes zero.

What is the relationship between the time period of a simple pendulum and its length?

  • The time period is proportional to the square of the length.
  • The time period is directly proportional to the length. (correct)
  • The time period is inversely proportional to the square of the length.
  • The time period is inversely proportional to the length.

What is the relationship between the time period of a simple pendulum and its mass?

<p>The time period is independent of the mass. (C)</p> Signup and view all the answers

What happens to the time period of a simple pendulum when the acceleration due to gravity increases?

<p>The time period decreases. (C)</p> Signup and view all the answers

A hollow sphere filled with water is hung by a long thread and the water is allowed to slowly flow out of a small hole at the bottom. What happens to the time period of oscillation as the water flows out?

<p>The time period increases then decreases. (D)</p> Signup and view all the answers

What is the primary factor that affects the time period of oscillation of a simple pendulum?

<p>Length of the pendulum (A)</p> Signup and view all the answers

According to the context, which of the following statements is true about Miss Dema's favorite game?

<p>The game involves a swinging object. (B)</p> Signup and view all the answers

What does a higher spring constant indicate in terms of spring behavior?

<p>More force is required to compress the spring. (D)</p> Signup and view all the answers

Which factor is most directly related to a spring's restoring force according to Hooke's law?

<p>The spring constant. (D)</p> Signup and view all the answers

What is necessary to achieve a good suspension system setup in a car?

<p>Balancing stiffness and comfort (C)</p> Signup and view all the answers

In terms of vehicle dynamics, what happens as the spring constant decreases?

<p>The car becomes less responsive to steering. (A)</p> Signup and view all the answers

In a simple harmonic motion equation, when is the kinetic energy at its maximum?

<p>At the mean position (A)</p> Signup and view all the answers

If both potential energy and kinetic energy are equal in SHM, what can be inferred about the amplitude 'A'?

<p>A is $ rac{PE}{2}$ (C)</p> Signup and view all the answers

For greater stability in a car, the suspension system should ideally possess what characteristic?

<p>A greater spring constant. (B)</p> Signup and view all the answers

Why might a laboratory worksheet record timing for 20 oscillations instead of one?

<p>To ensure error minimization in measurement (C)</p> Signup and view all the answers

What does the acceleration equation a = -ω²A imply about the movement of the mass?

<p>Acceleration is dependent on the angular frequency. (D)</p> Signup and view all the answers

How does a stiffer suspension system affect a car during cornering?

<p>It allows the car to feel more responsive. (C)</p> Signup and view all the answers

What is the total energy in simple harmonic motion represented by?

<p>TE = kA2 (A)</p> Signup and view all the answers

What is the consequence of selecting a less stiff spring for a vehicle?

<p>Increased weight transfer during cornering. (B)</p> Signup and view all the answers

In the setup of a pendulum in SHM, what factors determine the restoring force?

<p>The displacement of the pendulum (B)</p> Signup and view all the answers

Which relationship does the formula k = mω² describe?

<p>The relationship between mass, angular frequency, and spring constant. (A)</p> Signup and view all the answers

At what position does the kinetic energy of a toy undergoing SHM equal its potential energy?

<p>At A from the mean position (D)</p> Signup and view all the answers

Which of the following statements about kinetic energy and potential energy in SHM is true?

<p>Potential energy is maximum and kinetic energy is minimum at extreme positions (A)</p> Signup and view all the answers

What will happen to the period of a simple pendulum if a little mercury is drained off?

<p>Increases (C)</p> Signup and view all the answers

What type of oscillation occurs when a body vibrates with its own natural frequency?

<p>Free oscillation (A)</p> Signup and view all the answers

What is the relationship between the period and the angular frequency of an oscillating system?

<p>Period is the inverse of angular frequency (C)</p> Signup and view all the answers

If the total energy of a system executing simple harmonic motion is 5.83 J, what does this energy primarily consist of?

<p>Total kinetic and potential energy (C)</p> Signup and view all the answers

How is the spring constant related to the mass and the period of an object executing simple harmonic motion?

<p>It is inversely proportional to the square of the period (D)</p> Signup and view all the answers

What effect does an increase in amplitude have on the maximum velocity of a simple harmonic oscillator?

<p>Increases the maximum velocity (D)</p> Signup and view all the answers

If a block weighing 4 kg extends a spring by 0.16 m, what is the force constant of the spring?

<p>25 N/m (A)</p> Signup and view all the answers

What does not affect the period of a simple pendulum?

<p>Mass of the bob (A)</p> Signup and view all the answers

What is the expression for the velocity of a particle executing simple harmonic motion?

<p>$V = ωA \cos(ωt)$ (D)</p> Signup and view all the answers

In simple harmonic motion, what relationship describes acceleration in terms of displacement?

<p>$\beta = -ω^2 y$ (C)</p> Signup and view all the answers

If the displacement of a particle in SHM is given by $x = 0.25 \cos(\frac{π}{8}t)$, what is its amplitude?

<p>0.25 m (B)</p> Signup and view all the answers

What is the formula used to determine the maximum speed of a particle in SHM?

<p>$V_{max} = ωA$ (B)</p> Signup and view all the answers

When a particle in SHM is at a distance of 2 cm from its mean position, what is the formula to find its velocity?

<p>$v = ω \sqrt{A^2 - 2^2}$ (B)</p> Signup and view all the answers

In the equation for angular frequency of SHM, what does the variable ω represent?

<p>Angular frequency (A)</p> Signup and view all the answers

Given the displacement function $y = 0.2 \sin(50πt + 1.57)$, what is the angular frequency?

<p>50 rad/s (D)</p> Signup and view all the answers

What is the formula for calculating the time period (T) of an object in SHM?

<p>$T = \frac{2π}{ω}$ (B)</p> Signup and view all the answers

What is the amplitude of the resultant SHM for the displacement equation: 𝑥 = 6𝑐𝑜𝑠𝜔𝑡 + 8𝑠𝑖𝑛𝜔𝑡 ?

<p>10 m (B)</p> Signup and view all the answers

What is the phase angle () of the resultant SHM for the displacement equation: 𝑥 = 6𝑐𝑜𝑠𝜔𝑡 + 8𝑠𝑖𝑛𝜔𝑡 ?

<p>53.1° (A)</p> Signup and view all the answers

What is the equation for the potential energy (PE) of a spring in simple harmonic motion (SHM)?

<p>PE = 1/2 * k * x² (B)</p> Signup and view all the answers

What does the term 'k' represent in the equation F = -kx, which describes Hooke's Law?

<p>spring constant (A)</p> Signup and view all the answers

What is the relationship between potential energy and kinetic energy in simple harmonic motion (SHM)?

<p>Potential energy is maximum when kinetic energy is minimum, and vice versa. (A)</p> Signup and view all the answers

What is the formula for the kinetic energy (KE) of an object in simple harmonic motion (SHM)?

<p>KE = 1/2 * m * v² (D)</p> Signup and view all the answers

What is the expression for the velocity of an object in simple harmonic motion (SHM), given its amplitude (A), angular frequency (ω), and displacement (x)?

<p>v = -ωA sin(ωt) (D)</p> Signup and view all the answers

The time period of a combination of periodic functions is equal to:

<p>The smallest time period among all functions (A)</p> Signup and view all the answers

Flashcards

Simple Harmonic Motion (SHM)

A type of oscillation where a particle moves back and forth around an equilibrium position.

Displacement Equation

The position of a particle in SHM can be described by x = A sin(ωt).

Velocity in SHM

The velocity of a particle in SHM is given by V = ωA cos(ωt).

Acceleration in SHM

The relationship between acceleration (β) and displacement (y) is β = -ω²y.

Signup and view all the flashcards

Maximum Speed

The maximum speed in SHM is given by V_max = ωA.

Signup and view all the flashcards

Amplitude

The maximum extent of displacement from the equilibrium position in SHM.

Signup and view all the flashcards

Angular Frequency

The rate of oscillation in SHM, denoted by ω, measured in radians per second.

Signup and view all the flashcards

Time Period

The time taken for one complete cycle of motion in SHM, denoted by T.

Signup and view all the flashcards

Resultant amplitude (D)

The combined amplitude from two waves given by D = √(A² + B²).

Signup and view all the flashcards

Phase angle (φ)

The phase difference between two periodic functions calculated as φ = tan⁻¹(B/A).

Signup and view all the flashcards

Potential Energy (PE)

Energy stored due to the position of an object, PE = (1/2) kx² in SHM.

Signup and view all the flashcards

Kinetic Energy (KE)

Energy of motion given by KE = (1/2) mv², with v being the velocity.

Signup and view all the flashcards

Hooke's Law

States that the restoring force (F) is proportional to displacement (x): F = -kx.

Signup and view all the flashcards

Superposition of waves

The principle where two or more waves combine to form a resultant wave.

Signup and view all the flashcards

Time period of periodic functions

The time taken for one complete cycle of the wave; equal to the minimum of combined periods.

Signup and view all the flashcards

Spring Constant (k)

A measure of a spring's stiffness; relates force to displacement.

Signup and view all the flashcards

Hooke’s Law

The principle stating that force is proportional to displacement: F = -kx.

Signup and view all the flashcards

Potential Energy in Springs

PE = (1/2) k A² cos²(ωt) describes energy stored in a spring.

Signup and view all the flashcards

Kinetic Energy in Springs

KE = (1/2) m (−ω A sin(ωt))² represents energy in motion.

Signup and view all the flashcards

Car Suspension Stiffness

Determined by the spring constant; affects stability and comfort.

Signup and view all the flashcards

Effect of Stiffer Springs

Increases stability by reducing body roll and weight transfer.

Signup and view all the flashcards

Effect of Softer Springs

Leads to more body roll and weight transfer, reducing stability.

Signup and view all the flashcards

Trade-off in Suspension

Stiffer springs improve stability but may reduce ride comfort.

Signup and view all the flashcards

Force on Pendulum

F = mg sin(θ) represents the force acting on a pendulum.

Signup and view all the flashcards

Small Angle Approximation

For small angles, sin(θ) ≈ θ, simplifying calculations.

Signup and view all the flashcards

Pendulum Period Formula

T = 2π √(L/g) describes the oscillation period of a pendulum.

Signup and view all the flashcards

Center of Mass (CM) Shift

CM moves as water flows out, affecting pendulum length.

Signup and view all the flashcards

Effective Length

The effective length of a pendulum is tied to its oscillation period.

Signup and view all the flashcards

Period Increase with Water

Initial outflow of water increases the pendulum period as CM drops.

Signup and view all the flashcards

Period Decrease with Water

As CM rises after water is emptied, the pendulum period decreases.

Signup and view all the flashcards

Newton's Law Application

F=ma is fundamental to understanding pendulum motion.

Signup and view all the flashcards

Suspension system balance

The equilibrium between stiffness and comfort in a car's suspension.

Signup and view all the flashcards

Spring constant

A value that determines the stiffness of the suspension spring, based on the car's weight.

Signup and view all the flashcards

Total Energy in SHM

The sum of potential energy (PE) and kinetic energy (KE) in simple harmonic motion.

Signup and view all the flashcards

Maximum KE and PE positions

KE is maximum and PE is minimum at the mean position; the opposite at extreme positions.

Signup and view all the flashcards

Frequency of oscillation

The number of complete cycles of motion per unit time in simple harmonic motion.

Signup and view all the flashcards

Mechanical energy in SHM

The total mechanical energy remains constant, varying between kinetic and potential energy.

Signup and view all the flashcards

Equal PE and KE

Occurs at a distance of A/√2 from the mean position in SHM.

Signup and view all the flashcards

Time period of a pendulum

The time taken for one complete cycle of motion in a pendulum or spring system.

Signup and view all the flashcards

Maximum Velocity Formula

The maximum velocity in SHM can be calculated using V_max = ωA.

Signup and view all the flashcards

Amplitude in SHM

The maximum displacement of a particle in simple harmonic motion from its equilibrium position.

Signup and view all the flashcards

Angular Speed (ω)

Angular speed in SHM is given by ω = 2π/T, where T is the time period.

Signup and view all the flashcards

Time Period (T)

Time taken for one complete cycle of motion in SHM, denoted by T.

Signup and view all the flashcards

Frequency in SHM

Frequency is the number of cycles per second, f = 1/T.

Signup and view all the flashcards

Natural Angular Frequency

The frequency at which a system oscillates freely when disturbed: ω = √(k/m).

Signup and view all the flashcards

Study Notes

Summary of Provided Images

  • Images display various physics concepts, including welcome messages, topic headings, equations, diagrams, tables, and descriptions related to oscillations.
  • Topics covered include:
    • Introduction to Class XII Physics - 2024
    • Time allocation & weighting for topics
    • Definition of periodic motion and oscillatory motion
    • Scope of oscillatory motions, including simple harmonic motion.
    • Characteristics of oscillatory motion (restoring force, energy conservation)
    • Simple harmonic motion (SHM)
    • Velocity and acceleration in SHM
    • Phase of SHM
    • Time period and frequency
    • Numerical problems related to SHM
    • Relation of SHM to uniform circular motion
    • Graphical representation of displacement, velocity, and acceleration in SHM.
    • Energy in SHM.
    • Comparing concepts like resonance in relation to oscillations or natural frequency.
    • Examples of simple harmonic motion in mechanics (pendulum)
    • Problems on calculating amplitude, frequency, time period.
    • Discussion on various types of problems, and different types of oscillations.
    • Practical applications of simple harmonic motion and oscillations.
  • The images include diagrams, equations, and descriptions related to these topics, as well as experimental setup and table(s) for collecting observations.
  • The images suggest a course or lecture covering all sections.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Introduction to Class XII Physics - 2024 PDF

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser