Can the energy method for this system be represented in a matrix form?

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SUMMARY

The discussion focuses on representing kinetic energy (T) and potential energy (V) of a mechanical system in matrix form. The kinetic energy is expressed as T = 1/2 (q'^T) * (2 0; 0 m2) and the potential energy as V = 1/2 (q^T) * ((5+k2) -k2; -k2 k2). The parameters involved include mass m1 = 2, spring constant k1 = 5, and variables m2 and k2. The matrix representations provided are confirmed to be correct based on the equations outlined.

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JI567
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Hi,

Can somebody tell me if my kinetic energy (T) and potential energy of spring (V) for this system in matrix form is correct or wrong,

m1= 2, k1 =5, m2 = m2, k2 = k2

T = 1/2 (2* q1'^2+ m2* q2'^2) so in matrix form it was 1/2(q'^T) (2 0 *( q')
0 m2)
V = 1/2 (5*q1^2+k2(q2-q1)^2) = 1/2 ((5+k2)* q1^2- 2*k2*q1*q2 + k2*q2^2) so in matrix form it was

1/2 (q^T) ( 5+k2 -k2 * (q)
-k2 k2)
upload_2014-11-17_18-7-20.png
 
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The matrix for T is
2 0
0 m2
 
The Matrix for V is

5+k2 -k2
-k2 k2
 

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