{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

20. Ch6_1D_wave_equation_linear_displacement

# 20. Ch6_1D_wave_equation_linear_displacement -...

This preview shows pages 1–3. Sign up to view the full content.

6.1.2 1D wave equation: arbitrary initial displacement of the string (i) Orthogonality of the eigenfunctions ׬ ݏ݅݊ గ௫ ቁ ݀ݔ ് 0 ׬ ݏ݅݊ ቀ గ௫ ቁ ݏ݅݊ ቀ ଶగ௫ ቁ ݀ݔ ൌ 0 ׬ ݏ݅݊ ቀ గ௫ ቁ ݏ݅݊ ቀ ଷగ௫ ቁ ݀ݔ ൌ 0 ׬ ݏ݅݊ ቀ గ௫ ቁ ݏ݅݊ ቀ ସగ௫ ቁ ݀ݔ ൌ 0 0 0.5 1 term 1: sin 2 ( π x/L) 1 0.5 0 0.5 1 term 2: sin ( π x/L) sin (2 π x/L) 1.5 1 0.5 0 0.5 1 term 3: sin ( π x/L) sin (3 π x/L) 1.5 1 0.5 0 0.5 1 term 4: sin ( π x/L) sin (4 π x/L) x L x L x L x L

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
(ii) Comparison of the solution at t =0 and IC term 1: 2/( π ) sin ( π x/100) term 2: 2/(2 π ) sin (2 π x/100) term 3: 2/(3 π ) sin (3 π x/100) term 4: 2/(4 π ) sin (4 π x/100) term 5: 2/(5 π ) sin (5 π x/100) term 10: 2/(10 π ) sin (10 π x/100) Solutionat t = 0, keeping 10 terms in the infinite series s ( x ,0) term1 – term2 + term3 term10 Solution at t = 0 with infinite terms gives the exact IC ࢞, ૙ ૛ࡴ െ૚
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

20. Ch6_1D_wave_equation_linear_displacement -...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online