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(C) Resonance energy is directly proportional to the extent of conjugation in the molecule.$(I)$ $CH_2=CH-CH=CH-OCH_3$ has a system of $4$ conjugated

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$I > II > III$

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(C) Resonance energy is directly proportional to the extent of conjugation in the molecule.$(I)$ $CH_2=CH-CH=CH-OCH_3$ has a system of $4$ conjugated $\pi$-bonds (including the lone pair on oxygen),which provides extended conjugation.$(II)$ $CH_2=CH-C(OCH_3)=CH_2$ has a cross-conjugated system.$(III)$ $CH_2=CH-OCH_3$ has only $2$ conjugated $\pi$-bonds.Therefore,the extent of conjugation is $I > II > III$,which implies the order of resonance energy is $I > II > III$.

For the given compounds,the correct order of resonance energy is:
$(I)$ $CH_2=CH-CH=CH-OCH_3$
$(II)$ $CH_2=CH-C(OCH_3)=CH_2$
$(III)$ $CH_2=CH-OCH_3$

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For the given compounds,the correct order of resonance energy is:$(I)$ $CH_2=CH-CH=CH-OCH_3$$(II)$ $CH_2=CH-C(OCH_3)=CH_2$$(III)$ $CH_2=CH-OCH_3$