Role of voltage source in relaxation oscillator
You can &quot;thwack&quot; a coil and make it oscillate, but it'll run out of energy.  Nothing is perfect, so energy gets lost with every oscillation cycle.  Because of this lost energy, the coil needs to get &quot;thwacked&quot; periodically so that oscillation will continue.
The battery is there to provide those &quot;thwacks&quot; to start the oscillation, and to make it continue by making up the energy lost in the resistors.
No battery, no oscillation.