Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. 7.7.3. consider a vibrating quarter-circular membr

7.7.3. Consider a vibrating quarter-circular membrane, 0 < r < a,0 < ? < ?/2, with...

90.2K

Verified Solution

Question

Advance Math

7.7.3. Consider a vibrating quarter-circular membrane, 0 < r< a,0 < ? < ?/2, with u =0 on the entire boundary. [Hint:You may assume without derivation that ?>0 and that productsolutions
u(r,?,t)=?(r,?)h(t)=f(r)g(?)h(t)
satisfy
?2?+?? =0 dh dt =??kh d2g d?2 =??g
r
d drrdf dr+(?r2 ??)f =0 .]

*(a) Determine an expression for the frequencies ofvibration.

(b) Solve the initial value problem if u(r,?,0) = g(r,?), ?u ?t(r,?,0) = 0.

(c) Solve the wave equation inside a quarter-circle, subject tothe conditions
?u ?r
(a,?,t)=0,u (r,0,t)=0 ur, ? 2,t=0,u (r,?,0) = 0 ?u ?t (r,?,0) =?(r,?)

Answer & Explanation Solved by verified expert
3.7 Ratings (339 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: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Statistics
1.2K views

You may need to use the appropriate appendix table or technology to answer this question. A simple...

Operations Management
1.2K views

D4/MIS: Please make sure the answer should be in your won words. I would appreciate if...

Advance Math
1.2K views

3. In R4 , does the set {(1, 1, 1, 0,(1, 0, 0, 0),(0, 1, 0,...

Calculus
1.2K views

Describe the intervals on which the functionf (x) = ln | x| is continuous. Are...

Calculus
1.2K views

Match equation question type with a graph x A x B y y y x...

Calculus
1.2K views

An auditorium with a flat floor has a large screen on one wall The lower...

Accounting
1.2K views

Please how can i do this. Thank Multiple Choice Question 93...

Accounting
1.2K views

Crumbley Inc. produces and sells two products. Data concerning those products for the most recent...

Accounting
1.2K views

3_6 Accrual-basis accounting versus cash-basis accounting for...

Finance
1.2K views

6. Midwest Power and Light operates 14 coal-fired power plants in several states around the...

Accounting
1.2K views

Companies often choose to keep an unprofitable product line, segment, or department. Why is this...

Finance
1.2K views

Sole proprietorship is an unincorporated business owned by an individual who usually also manages it....