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# hwk02 - Chapter 2 Solution RQ1 The period of the vibration...

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1 Chapter 2 Solution RQ1. The period of the vibration is the minimum time necessary for the motion to repeat itself. The period is the reciprocal of the frequency. RQ3. In a vibrating system, if the restoring force was proportional to the displacement, then the motion is the simple harmonic motion. Simple harmonic motion is a repetitive motion, exactly the same each cycle and with one frequency. RQ5. Potential energy is proportional to the square of the distance. So, if we double the distance, the potential energy is increased by a factor of 4. RQ9. If the masses were free to move in all three coordinate directions, 4-mass system will have 4 modes of longitudinal vibration and 8 modes of transverse vibration. Fig. 1(a) shows the 4 longitudinal modes and Fig. 1(b) shows one set of the transverse modes. Because transverse motion can move in two dimensions, the total modes of transverse vibration are 8. Fig.1: (a) Modes of longitudinal vibration for 4-mass system. (b) One set of modes of transverse vibration for 4-mass system.

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