All the families/clans of the same family name do not always use the same, only one family crest/kamon. Sorry to inform this, but it's impossible to investigate your kamon only by that information, except when your family is well-known, like a daimyō clan.
A while back , I was reading about family Kamon's on Google and I was surprised how many had 5 or 6 possibilities to pick from. I think one comment was about very old gravestones sometimes had the family Kamon on them.
Yes, if Jutaro knows where his ancestors are buried, he might find his family's kamon on their gravestones. (Or, if really lucky, we might be able to find them using google maps, but its a bit unlikely). Other places he might find it are on family heirlooms like kimono.
But if somebody says, "My last name is Tanaka, please tell me what m kamon is", it would be impossible. There are Tanakas found all across Japan, and there are many, many kamon associated with the name Tanaka (or Watanabe, or Sato, or Saito, or most any Japanese name).