Recent Lessons

Show all results for ""

Feature Overview

Ace your exams with our all-in-one platform for creating and sharing quizzes and tests.

Quizzes

Create quizzes and tests automatically from your content using AI.

Flashcards

Automatically turn your notes into digital flashcards.

Share, Export & Embed

Share with classmates or export to Excel and your learning management system.

Stats & Reporting

Auto-grading quizzes and tests with detailed stats and reports.

Mobile Apps

The smarter way to study – wherever you are.

Pricing

Search...

5 Questions

5 Views

Simple Harmonic Motion Quiz

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 expression for the energy at time t in damping motion?

E(t) = Eo e^{-2bt} (correct)

E(t) = Eo e^{bt}

E(t) = Eo e^{2bt}

E(t) = Eo e^{-bt}

What is the expression for the logarithmic decrement of amplitude of a damped oscillator?

ln(Ad) = ln(P) * bt

ln(Ad) = ln(P) / bt

ln(Ad) = ln(P) + bt

ln(Ad) = ln(P) - bt (correct)

What is the relationship between successive amplitudes A3 and A4 of a damped oscillator?

A4 = Ao e^{-b(3T+T/4)} (correct)

A4 = Ao e^{-b(2T+T/4)}

A4 = Ao e^{-bT/4}

A4 = Ao e^{-b(T+T/4)}

What does the constant ebT represent in the context of a damped oscillator?

<p>Decay constant</p> Signup and view all the answers

At what time t does the amplitude A1 of a damped oscillator reach Ao e^{-bT/4} if the oscillator starts from its mean position?

<p>t = T/4</p> Signup and view all the answers

Study Notes

Simple Harmonic Motion (SHM)

SHM is a type of periodic motion that repeats after a definite time interval.
The amplitude of oscillation is small, and the damping is smaller than the oscillation frequency (b < ω).

Damped Oscillation

The equation of motion for damped oscillation is x = e^(-bt) [A cos(ω² - b² t) + B sin(ω² - b² t)].
The amplitude of oscillatory damped oscillation is not constant, but it dies away exponentially (P e^(-bt)).
The oscillatory function is x = P e^(-bt) cos(ω² - b² t - ψ).

Undamped SHM

When b = 0, the equation of motion becomes x = P cos(ωt - ψ), which is the solution for free/undamped SHM.

Conclusions

The amplitude of oscillatory damped oscillation decreases exponentially with time.
The frequency of oscillation is affected by the damping factor (b).

Studying That Suits You

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

Description

Test your knowledge of Simple Harmonic Motion (SHM) with this quiz. Explore the concepts of periodic motion, oscillation, amplitude, and damping in SHM.