Berdasarkan rujukan pertama di bawah ini,

appreciate = mengetahui, menyadari

Sekarang, kalau dimasukkan ke kalimat pada rujukan kedua,

Sekarang diketahui bahwa perhitungan akurat tingkat getaran itu sulit.

Begitu pula dg kalimat pada rujukan ketiga,

Ini dapat diketahui dg membandingkan dst.

Karena itu, saya mengusulkan padanan:

appreciated = yang diketahui

Dg menimbang struktur kalimat sumber:

amplitude and frequency are variable with both low frequency/high amplitude vibration appreciated.

amplitudo dan frekuensi tidak tetap pada getaran frekuensi rendah maupun getaran amplitudo tinggi yang diketahui.
Rujukan:
Appreciate = 1. To recognize the quality, significance, or magnitude of: appreciated their freedom.
2. To be fully aware of or sensitive to; realize: I appreciate your problems.
http://www.thefreedictionary.com/appreciate

It will be appreciated by now that accurate calculation of vibration levels is difficult.
https://books.google.co.id/books?id=xfrCzxP_erUC&pg=PA272&lp...

This can be appreciated by comparing the patterns of peak amplitudes in Fig. 1 (c) against those in Fig. 8 (c).
http://www.ece.rochester.edu/people/faculty/parker_kevin/ass...

amplitude and frequency are variable with both low frequency/high amplitude vibration appreciated = amplitudo dan frekuensi adalah variabel yang dengan keduanya getaran frekuensi rendah/amplitudo tinggi (dapat) dirasakan (oleh kita).
IMO.

appreciated dalam konteks kalimat "amplitude and frequency are variable with both low frequency/high amplitude vibration appreciated" adalah angka atau nilai dari variable amplitude & frequency.

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Note added at 1 day2 hrs (2016-01-10 09:31:41 GMT)
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maaf typo, seharusnya di-assess.