本文旨在研究非線性軟彈簧系之穩態振幅受到外力作用下所產生之跳躍現象(Jump Phenomena)。
本研究進行三組分析，第一組為外力頻率持續改變下，初始條件維持在零，觀察其跳躍現象；第二組為設計兩組持續改變頻率之外力接續而成，觀察其跳躍現象；第三組是將初始條件擴展至二維度，將對應之穩態振幅繪成二維振幅圖，藉由顏色與圖形之變化探討初始值對穩態振幅之影響；最後再將非線性軟彈簧系統之跳躍現象與Duffing硬彈簧系統比較。由三組分析可以得知跳躍現象只會在特定頻率比範圍發生，並沒有固定的跳躍模式且發生的頻率比是由初始條件決定，如果頻繁的改變初始條件，跳躍現象可能發生不只一次。

The purpose of this syudy is to dicuss the jump phenomenon of nonlinear softening system under the external force. In order to discuss the jump phenomenon, there are three different analyses in this study.
To observe the jump phenomenon, the first analysis maintains the initial condition at zero and change external force frequency continuously；the second analysis designs two sets of simulations that continuously change external forces；the last analysis extends the initial conditions from zero to second dimension, then plot the two-dimensional amplitude figure. The result of the three analyses shows that jump up and jump down phenomena occur in different frequency ratio is because of the initial conditions, and also may occur not only once. At the end of the study compares the jump phenomenon of the Nonlinear softening system with Duffing hardening system.

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