How do I get the transfer functions of the following block diagrams

a) [K(s+a)/(s+1)]--->[1/s(s+2)(s+3)]
........BLOCK 1.............BLOCK 2

b) [4+(40/s)]--->[s^2/(s+100)(4s^2+5s+4)]
.....BLOCK 1..................BLOCK 2

c) [a+(B/s)]---->[1/(s+1)]
.....BLOCK 1........BLOCK 2

 

If the blocks are simply in series (one directly after the other with no feedback), then the answer is really simple: all you have to do is multiply the blocks.

For example, if your block diagram looks like:

R --> | G | --> | H | --> Y

where R is the input, Y is the output and G and H are blocks (with corresponding transfer functions), then all you do to get the signal at each point is multiply the previous signals/blocks: so Y = H*G*R, so your transfer function is output/input = Y/R = H*G.

 

yes they are all in series with no feedback, b) was asked for the open loop. Is that any different

 

It's exactly the case kevinarms described.