在許多領域中，如物理、化學、以及生物科學等，測量微小物體的質量都是相當重要的。其中有一種測量方法，是利用懸臂樑的自然頻率變化。當我們在懸臂樑上放置一個物體時，由於質量的改變，會使得懸臂樑的自然共振頻率產生偏移。經由計算，可以將頻率偏移量轉換成放置物體的質量。本研究探討待測物體所放置的位置對於共振頻率的影響。此實驗使用奈米碳管做為測量用的懸臂樑，放上銀的奈米顆粒做為待測質量在超高真空穿透式電子顯微鏡上做即時量測。由實驗結果畫出銀奈米顆粒在懸臂樑上位置對共振頻率的變化曲線，並將實驗數據和古典力學推導之解析解做比較。本實驗所量測的質量精確度達到10-18 g的等級，成功的在奈米尺度下移動顆粒並量測共振頻率。

It is very important to measure a minute mass in many fields, of physical, chemical, and biochemical sciences. One of the methods to measure minute mass is using cantilever-based resonators. The method’s basic principle is to measure the mass sensor’s resonance frequency shift and translate the measurement into the mass of the mass load. In this study, we have investigated the influence of added mass of different positions experimentally, with in situ ultra high vacuum transmission electron microscopy, and compared the experiment results with analytical expression. This experiment uses carbon nanotube as cantilevers and silver nanoparticle as added mass. The cantilever’s frequency shift with an attached silver nanoparticle is verified experimentally, and is determined as a function of the nanoparticle position. The mass sensitivity for the carbon nanotube based resonators in our experiments is less than 10-18 g.

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