Do not shake. Circuit will autostart.
Two isolated sources on bottom are the there to visualize the circuit better.
Op-amp 1 : wein bridge Oscillator (Clamped Carrier)
Op-amp 2 : Amplifier with variable gain
The input signal varies the resistance of transistor which varies the Amplification Factor of op-amp 2.
The output wave has Modulation Index of 0.3 which can be increased by changing the voltage of input signal but increasing Modulation Index causes distortion in signal.
Your ideas are most welcome.