Logo
Home Study Material Contact Search
AI Chat FREE
  1. sciences
  2. physics
  3. a mass m=4 is attached to both a spring with sprin

A mass m=4 is attached to both a spring with spring constant k=145 and a dash-pot...

90.2K

Verified Solution

Question

Physics

A mass m=4 is attached to both a spring with spring constantk=145 and a dash-pot with damping constant c=4.

The ball is started in motion with initial position x0=1and initial velocity v0=6 .
Determine the position function x(t) .

x(t)=?

Note that, in this problem, the motion of the spring isunderdamped, therefore the solution can be written in the formx(t)=c1e^(-ρt)cos(ω1t-α1) .Determine c1, ω1, ρ and α1.

c1=?
ω1=?

ρ=?

α1=?

Graph the function x(t) together with the \"amplitude envelope\"curves x=-c1e^(-ρt) and x=c1e^(-ρt).

Now assume the mass is set in motion with the same initial positionand velocity, but with the dashpot disconnected ( so c=0). Solvethe resulting differential equation to find the position functionu(t).
In this case the position function u(t) can be written asu(t)=c0cos(ω0t-α0). Determinec0, ω0,and α0.

c0=?
ω0=?

α0=?

Answer & Explanation Solved by verified expert
3.8 Ratings (608 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Zin AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

Please fill out the Internal structures of the heart

Medical Sciences
Q

Mickey Johnson is considering investing some money that he inherited. The following payoff table gives the               profits...

Operations Management
Q

Which of the following molecules contains the strongest polar covalent bond? 02 H20 CH4 H2...

Biology
Q

How much would a 51.8 kg person weigh on the surface of Venus?Remember, weight is...

Physics
Q

5 Prepare journal entries to record the following merchandising transactions of Lowe s which uses...

Basic Math
Q

What is a counterexample of this statement? If a polygon is a trapezoid, then it...

Basic Math
Q

Aron of a sector of a circle The area of a sector of a circle...

Calculus
Q

A veteran may regain eligibility at the maximum entitlement if the purchaser is able to...

Algebra
Q

Which of the following is regarded as contributed capital? share capital retained earnings earned capital...

Accounting
Q

Sarbanes-Oxley Act. Why did congress pass the Sarbanes-Oxley Act? What is its purpose? How is...

Accounting
Q

The Rink offers annual $350 memberships that entitle members to unlimited use of ice-skating facilities...

Accounting
Q

1. Which one of the following might explain reporting negative net earnings and positive cash...

Finance