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3. (25 points) A spring-mass system (see figure), which is constrained to move in the vertical direction only. (a) Derive the equations of motion.

3. (25 points) A spring-mass system (see figure), which is constrained to move in the vertical direction only. (a) Derive the equations of motion. (b) Find the natural frequencies. (c) Find and sketch the mode shapes. m m k

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