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(i) 49s" + s = 0, s(0) = 24, s' (0) = 0. (ii) s" +9s = 0, s(0) = 6, s' (0) = 0. (iii) s" + 49s = 0, s(0) = 5, s' (0) = 0. (iv) 9s" + s = 0, s(0) = 12, s' (0) = 0. Which differential equation represents: (a) The spring oscillating most quickly (with the shortest period)? ? (b) The spring oscillating with the largest amplitude? ? ✓ (c) The spring oscillating most slowly (with the longest period)? ? (a) The spring oscillating with the largest maximum velocity? ?

(i) 49s" + s = 0, s(0) = 24, s' (0) = 0. (ii) s" +9s = 0, s(0) = 6, s' (0) = 0. (iii) s" + 49s = 0, s(0) = 5, s' (0) = 0. (iv) 9s" + s = 0, s(0) = 12, s' (0) = 0. Which differential equation represents: (a) The spring oscillating most quickly (with the shortest period)? ? (b) The spring oscillating with the largest amplitude? ? ✓ (c) The spring oscillating most slowly (with the longest period)? ? (a) The spring oscillating with the largest maximum velocity? ?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(i) \( 49s'' + s = 0, \, s(0) = 24, \, s'(0) = 0 \). (ii) \( s'' + 9s = 0, \, s(0) = 6, \, s'(0) = 0 \). (iii) \( s'' + 49s = 0, \, s(0) = 5, \, s'(0) = 0 \). (iv) \( 9s'' + s = 0, \, s(0) = 12, \, s'(0) = 0 \). Which differential equation represents: (a) The spring oscillating most quickly (with the shortest period)? \(\boxed{?}\) (b) The spring oscillating with the largest amplitude? \(\boxed{?}\) (c) The spring oscillating most slowly (with the longest period)? \(\boxed{?}\) (d) The spring oscillating with the largest maximum velocity? \(\boxed{?}\)
Transcribed Image Text:(i) \( 49s'' + s = 0, \, s(0) = 24, \, s'(0) = 0 \). (ii) \( s'' + 9s = 0, \, s(0) = 6, \, s'(0) = 0 \). (iii) \( s'' + 49s = 0, \, s(0) = 5, \, s'(0) = 0 \). (iv) \( 9s'' + s = 0, \, s(0) = 12, \, s'(0) = 0 \). Which differential equation represents: (a) The spring oscillating most quickly (with the shortest period)? \(\boxed{?}\) (b) The spring oscillating with the largest amplitude? \(\boxed{?}\) (c) The spring oscillating most slowly (with the longest period)? \(\boxed{?}\) (d) The spring oscillating with the largest maximum velocity? \(\boxed{?}\)
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