Transfer function for amplitude modulation

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What is the transfer function of the amplitude modulation element where the output is simply the input multiplied by a sinusoidal wave with a constant amplitude?

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You could use:

$$ G(s) = \frac{\omega s}{s^2 + \omega^2} $$

If you input a step to this transfer function the output will be a sinusoidal wave with frequency $\omega = 2 \pi f$ and the amplitude equal to the height of the step.

Here a plot with 2 Hz:

enter image description here