system dynamics and vibration homework

I don’t understand this Engineering question and need help to study.

6 questions.

example:

Question 3 (Modes of vibrating systems). Consider the system shown in Figure 3.

  1. (a) The masses are m1 = 10 kg and m2 = 30 kg. The spring constants are k1 = 104 N/m and k2 = 2 × 104 N/m. Calculate the natural frequencies and the mode ratios (A1/A2) of the system.
  2. (b) Explain the meaning of the mode ratios in relation to how the masses move relative to each other and the frequencies at which these motions occur.
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