See, in this case you want to use a router because you're creating a LAN (local area network) to connect to the WAN (wide area network [internet]) so in order to have 2 computers work at the same time on 1 cable modem which accepts 1 ip address, you would need to use the router to act as 1 IP address which then would serve your 2 computers requests out as 1 computer (via the router acting as 1 computer) to the internet, thus allowing both to work. the switch would allow 1 computer to work, normally the first one to be turned on and accept the new IP address while the second would drop off the workgroup (network connection).
Riser