If you don't need to isolate the two circuits, you can do as deepak george suggested and use a transistor to switch the oscillator. The 1K resistor and 2N3904 are just guesses, as I don't know what the peak oscillator current will be. If you want to control the pulse period and the pulse frequency independently, you will need two 555, or a 556. One as an astable followed by one as a monostable.
Ken