Many damped physical systems found in engineering may have their behaviour expressed by second-order non-homogeneous ordinary differential equations (ODES.) This type of problem involves obtaining the response of the associated homogeneous ODE and a particular solution for the non-homogeneous ODE. The sum of these two provides the general solution to the non- homogeneous ODE. Based on this information: EXPLAIN the physical meaning of the solution of the associated homogeneous ODE I)

Q: H6

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Q: Solve Parts a , b & c

A: (a) conduction current

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Helmholtz Free Energy

The Helmholtz free energy is a thermodynamic potential used to calculate the measure of useful work from a closed system. This system is kept at constant temperature and volume. German physicist Hermann Helmholtz introduced this concept in 1882.