Calculate the constants b₁ and b2 in the the following equation x(t)=b₁ cos k μl + b₂ sin μl for the condition (0) = max, the maximum extension of the oscillator. What is v(0) for this condition? Match the items in the left column to the appropriate blanks in the equations on the right. Make certain each equation is complete before submitting your answer.
Calculate the constants b₁ and b2 in the the following equation x(t)=b₁ cos k μl + b₂ sin μl for the condition (0) = max, the maximum extension of the oscillator. What is v(0) for this condition? Match the items in the left column to the appropriate blanks in the equations on the right. Make certain each equation is complete before submitting your answer.
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics
Section: Chapter Questions
Problem 7.1P
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Transcribed Image Text:Calculate the constants b₁ and b2 in the the following equation
1
Imax
d²x(t)
for the condition (0) ) = xmax, the maximum extension of the oscillator. What is v(0) for this condition?
Match the items in the left column to the appropriate blanks in the equations on the right. Make certain each equation is complete before submitting your answer.
?).
dt²
∞
b₂
0
t=0
dx (t)
(da)₁-0
dt
t=0
b₁
x(t)
v(0)
= xmax = b₁ co
Therefore, b₁ =
0
+ b₂ sin
and b₂ =
(√5.0)
k
μl
• (√) +0
k
COS
00 (√5-0)
x(t) = b₁ cos
Reset
t + b₂ sin
2 sin (√)
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