Electronic – How to prevent microphone from picking up movement

I doubt that you will find a microphone with a flat response to DC. Simple logic will tell you this :

From this page:

• Standard atmospheric pressure is 101,325 pascals
• 94dBa (loud!) = 1 Pa
• My local weather forecast is for an air pressure of 950mb (95% of standard pressure) this coming Saturday night (apologies to later readers, weather does vary!)
• That is an amplitude of 101,325 * 0.05 = 5066 Pa
• or a peak SPL of 168 dBa if you measure sound pressure down to DC.

Such a sound pressure level would damage any reasonably sensitive microphone : in practice there is a "leak" to the cavity behind the diaphragm to prevent such damage, and this necessarily limits the LF response.

If you REALLY need to measure down to DC, you will need to use a microphone down to 20Hz or so, then cross over to an atmospheric pressure sensor for frequencies lower than that.

But the revised question suggests that your application is probably better served by an accelerometer; you are looking to measure vibration (movement) rather than air pressure.

Adding to @GeorgeHerold's answer:

1. You need to include frequencies down to below 30Hz. Most of the energy in a typical heartbeat is between 30 and 40Hz. Given the cutoff for the highpass that @GeorgHerold computed, you are losing a good 15dB at the lower end.
2. Try using a directional microphone instead of an omnidirectional. Directional microphones have two openings, one in front and one in back by the solder pads. I find I get much better results by installing a directional mic such that the front (where you normally speak into the mic) is inside the tube, with the port on the back of the microphone out in open air.

Actually, I don't use a stethoscope in my experiments. A simple plastic shell with a hole in it for the microphone works very well. What I've used for this is a plastic cap like you would use to close one end of a plastic water line. I had some laying around that are about 2" in diameter, and they work well.

I find that a directional electret microphone installed in a platic cap as described works well enough that I can capture heart sounds using nothing more than a PC or smartphone with no additional electronics - I can then do filtering, recording, or other processing digitally.
The PC soundcard has a 20dB boost on the mic input, but the smartphones don't. Since the cards use 16Bit sampling, you have plenty of headroom to digitally amplify the signal even without using the boost. If you resample from 44100 down to 400 or so, then you could probably gain the equivalent of a few bits