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

AI Thread Summary
The discussion focuses on whether the kinetic energy (T) and potential energy (V) expressions for a given system can be accurately represented in matrix form. The kinetic energy is represented as T = 1/2 (q'^T) * (2 0; 0 m2) * q', while the potential energy is expressed as V = 1/2 (q^T) * (5+k2 -k2; -k2 k2) * q. Participants evaluate the correctness of these matrix representations based on the given parameters m1, m2, k1, and k2. The conversation emphasizes the importance of proper matrix formulation in representing energy equations in mechanical systems. Overall, the discussion seeks validation of the matrix forms for T and V.
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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