Electromagnetic energy harvesting designing problems
I'll assume your "10 mm amplitude" is peak to peak.  The position can therefore be described as

&nbsp;&nbsp;&nbsp;P = 5 sin(2&pi;12t) [mm]

or

&nbsp;&nbsp;&nbsp;P = 5 sin(&omega;t) [mm], where &omega; = 24&pi;

The velocity is the first derivative of position:

&nbsp;&nbsp;&nbsp;V = 5&omega; cos(&omega;t) [mm/s]

The acceleration is the second derivative of position and the first derivative of velocity:

&nbsp;&nbsp;&nbsp;A = -5&omega;2 sin(&omega;t) [mm/s2]

Plugging in our value of &omega;, the maximum acceleration is

&nbsp;&nbsp;&nbsp;Max A = 5&omega;2 mm/s2 = 5(24&pi;)2 mm/s2 = 28,400 mm/s2 = 28.4 m/s2 = 2.9 g

3 g isn't that much.  Of course you have to consider that this will be applied repetitively, but still, it should be possible to design something that can withstand many many 3 g cycles.