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b) An undamped oscillation under the influence of external: by UTM UTMUTM U m + kr dt2 where r(t) is the displacement at time t. Suppose a spring has mass m %3D UTMSUTM F) UTMU and spring constant k and let w F(t) = Focos (wot), where we # w. What type of value k and m so that the corresponding homogeneous solution is UTM UT with external force UTMUTM I(t) = A cos(wt) + B sin(wt)? Hence, by using the method of undetermined coefficients, show that UTM z(t) = A cos(wt) + B sin(wt) + UTM SUTM UTM UTM Fo TMUT UTMUTM m{w - -cos (t). aUTM UTMU UTM UT

b) An undamped oscillation under the influence of external: by UTM UTMUTM U m + kr dt2 where r(t) is the displacement at time t. Suppose a spring has mass m %3D UTMSUTM F) UTMU and spring constant k and let w F(t) = Focos (wot), where we # w. What type of value k and m so that the corresponding homogeneous solution is UTM UT with external force UTMUTM I(t) = A cos(wt) + B sin(wt)? Hence, by using the method of undetermined coefficients, show that UTM z(t) = A cos(wt) + B sin(wt) + UTM SUTM UTM UTM Fo TMUT UTMUTM m{w - -cos (t). aUTM UTMU UTM UT

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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Answer b
(t) = A cos(wt) + B sin(wt)? a) Solve the following differential equation 6UTM UTM UTM UT 5 UTM d'y d.r aTMUTM 5 UTE dr2 + 16y = 9e2 aUTM UTM UTM UTM UTM b) An undamped oscillation 5 UTMUT by UTM UTM U UTM is the displacement at time t. Suppose a spring has mass m + kr = di2 and spring constant k and let w 5UTMUTM S UTM F(t) = Fo cos (wot), where wo # w. What type of value k and m. so that the corresponding homogeneous solution is UTM UT with external force m 5 UTM UTM UTM Hence, by using the method of undetermined coefficients, show that UM UT x(t) = A cos(wt) +B sin(wt) + UTM UTM UTM UTM UTM Fo UTM UTM TM UT cos (unt). a UTM UTMU aUTM UT
Transcribed Image Text:(t) = A cos(wt) + B sin(wt)? a) Solve the following differential equation 6UTM UTM UTM UT 5 UTM d'y d.r aTMUTM 5 UTE dr2 + 16y = 9e2 aUTM UTM UTM UTM UTM b) An undamped oscillation 5 UTMUT by UTM UTM U UTM is the displacement at time t. Suppose a spring has mass m + kr = di2 and spring constant k and let w 5UTMUTM S UTM F(t) = Fo cos (wot), where wo # w. What type of value k and m. so that the corresponding homogeneous solution is UTM UT with external force m 5 UTM UTM UTM Hence, by using the method of undetermined coefficients, show that UM UT x(t) = A cos(wt) +B sin(wt) + UTM UTM UTM UTM UTM Fo UTM UTM TM UT cos (unt). a UTM UTMU aUTM UT
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