Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • You are riding in an automobile of mass 3000 kg .Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 15 cm when the entire automobile is placed on it. (b) the damping constant b

Q. 14.21 (b) You are riding in an automobile of mass 3000kg\;. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 15\; cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by 50^{o}/_{o} during one complete oscillation. Estimate the values of

(b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports750 \; kg..

Answers (1)

best_answer

The amplitude of oscillation decreases by 50 % in one oscillation i.e. in one time period.

\\T=2\pi \sqrt{\frac{m}{k}}\\ T=2\pi \times \sqrt{\frac{3000}{4\times 4.9\times 10^{4}}}\\ T=0.77\ s

For damping factor b we have

 

x=x_{0}e^{\left ( -\frac{bt}{2m} \right )}

x=x0/2

t=0.77s

m=750 kg

\\e^{-\frac{0.77b}{2\times 750}}=0.5\\ ln(e^{-\frac{0.77b}{2\times 750}})=ln0.5\\ \frac{0.77b}{1500}=ln2\\ b=\frac{0.693\times 1500}{0.77}\\ b=1350.2287\ kg\ s^{-1}

Posted by

Sayak

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Board Exams 2025: Counselling for students, parents from February 1
anam-khan

CBSE asks schools to include APAAR IDs in school ID after NTA says ‘not mandatory’ for NEET
anam-khan

CBSE Board Exams 2025: What the ethics code bans from exam centres

Latest Question