Browse by Stream
Discuss Doubts
Home
Search for Exam, Articles, Questions
get app
Go To Your Study Dashboard
  1. Home
  2. Stuck here, help me understand: - Oscillations and Waves - JEE Main-13
# Engineering

The displacement of a damped harmonic oscillator is given by 

x(t)=e^{-0.1t}cos(10\pi t +\phi )

Here t is in seconds. The time taken for its apmlitude of vibration

to drop to half of its initial value is close to:

  • Option 1)

    4\: s

  • Option 2)

    7\: s

  • Option 3)

    13\: s

  • Option 4)

    27\: s

 

Answers (1)
S solutionqc

 

Resultant amplitude in damped oscillation -

A=A_{0}.e^{-\frac{bt}{2m}}

E=E_{0}.e^{-\frac{bt}{m}}

- wherein

A= Amplitude

E= Energy

 

 

x(t)=e^{-0.1t}cos(10\pi t +\phi )

amplitude changes from A_o\: \: to\: \: \frac{A_o}{2}

=> \frac{A_o}{2}=A_oe^{-0.1t}

\ln 2=0.1t

t=\frac{\ln 2}{0.1}=\frac{0.7}{0.1}\approx 7sec


Option 1)

4\: s

Option 2)

7\: s

Option 3)

13\: s

Option 4)

27\: s

Similar Questions

Preparation Products

Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Test Series JEE Main April 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-
Buy Now
JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Test Series JEE Main April 2022

Take chapter-wise, subject-wise and Complete syllabus mock tests and get an in-depth analysis of your test..

₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
Start Now
 
Exams
Articles
Questions