This probably isn't your Melvin Ham, as all information points to him being a Melvin Eugene. But just in case the middle name of Frederick is wrong, here it is. Ancestry.Com has the birth of a Melvin Ham in Morgan County Ind on Nov 6, 1917: parents George and Lula Martin Ham.
Lula Martin married George Ham on Jan 6, 1912 in Morgan County.
there was a George Ham who registered for the WWI draft in Mogran County on June 5, 1917. born Aug 2, 1888 in V???ersburg Ind; married wife and 2 children; addres N. Main St Martinsville Ind. Other Hams who registered in Morgan County were Joseph J Ham dob Jan 17, 1888; and Marvin Edward Ham dob Jan 17, 1882. Joseph J and Marvin E Ham appear to be the sons of John M Ham on the 1900 MOrgan Cty Ind census.
There is this family: 1900 Fountain Cty Ind 165 169 Ham, Sam, Aug 1863 36 married 12 yrs Ettie, wife, Dec 1866 33 6 births 5 living Charley, son, June 1887 12 Georgie, son, Aug 1888 11 Haz??ll, dau Nov 1892 7 B?sthi? dau Nov 1898 2 (this is probably the Bertha Ham age 11, niece, in Henry W and Rachiel Neunum hh in 1910 Fountian Cty Ind census)
I suspect that this is the family: 1920 Morgan Cty Ind; Martinsville Ward l, dist 207; page 40 721 Mulberry 496 532 Hamm, Lulu 23, widow; Laundress at home Freda dau, 6 Earl W son 4 3/12 Melvin E, son 2 1/12 709 Mulberry 497 533 Martin, Orpha, 70 wid; In/Ky/Ky Harrison, son 30, In/In/In Looks like Lula remarried: Grover Lazell married Lula Hamm on Oct 2, 1920 in Marion Cty Ind. 1930 Morgan 153 15? Lazell, Grover, 3? Lulia, wife 34 Earl son 14 Melvin 12 Fe???, dau 10 Elmore 6 Norma 5 Sarahlow 2 Maren son 3/12
There is a Lula Martin, age 14, step dau of Fred Turk on the 1910 Morgan Cty Census; Fred Turk's wife is Melivinia and they had been married 3 yrears; siblings to Lula are Dollie M and Sarah E a Turk sister age 2.
There is a family tree posted at Ancestry.com that has Melvin Eugene Hamm as son of Lula May Lazell( Jan 28, 1895-Nov 30, 1988) and George Nathaniel Hamm (Aug 2, 1889-Dec 15, 1919) According to that tree Lula was Lula May Martin Hamm Lazelle, dau of John Franklin Martin and Lavina May Evans Martin Turk.