Springify a String

Python 2, 104 102 98 Bytes

f=lambda t:''.join((t+' '*13)[ord(x)-97+y*14]for y in range(len(t)/14+1)for x in'abgjklmhfedcgin')

Thanks for the comment help!

https://tio.run/#2VDVy

Original:

t=raw_input()+' '*13
print''.join(t[ord(x)-97+y*14]for y in range(len(t)/14)for x in'abgjklmhfedcgin')

JavaScript (ES6), 79 bytes

f=
s=>s.replace(/.{1,14}/g,s=>'0169abc7543268d'.replace(/./g,c=>s['0x'+c-0]||' '))

<input oninput=o.textContent=f(this.value)><pre id=o>

Hexadecimal string shamelessly stolen from @ETHproductions.

Jelly, 26 bytes

“4ṘƝ;þ¦Ɱ’b®¤ị
;⁶x14©¤s®ṖÇ€

TryItOnline!

How?

“4ṘƝ;þ¦Ɱ’b®¤ị - Link 1, output for a single coil: char array
           ¤  - nilad followed by link(s) as a nilad
“4ṘƝ;þ¦Ɱ’     - base 250 number, 13140239220751650
          ®   - retrieve from register (14 from main link)
         b    - convert to base, [1,2,7,10,11,12,13,8,6,5,4,3,7,9,0]
            ị - index into the char array

;⁶x14©¤s®ṖÇ€ - Main link: theString
      ¤      - nilad followed by link(s) as a nilad
 ⁶           - a space character
  x          - repeated
   14©       - place 14 into the register and yield 14
;            - concatenate theString with the 14 spaces
       s     - split into chunks of length
        ®    -     retrieve from register (14)
         Ṗ   - pop last entry from the result (removes the space only last entry of 14 chars or less)
          Ç€ - call the last link (1) as a monad for €ach
             - implicit print