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COUPLED OSCILLATORS There are two balls which have mass m. One of the balls is attached to a ceiling by a spring and the other ball is attached to the first ball with another spring, and hangs below Ball 1 as shown in the figure. The two springs have spring constant k, and an equilibrium length a. Motions in the z direction are the ones considered, and the gravitation force (of constant acceleration g) points in the negative z-axis. Contact interactions between the balls can be ignored. (i) For such a scenario, provide the equations of motion (ii) Provide the rest positions. iii) Finally, calculate the oscillation frequencies and give the general solutions to this problem (z1,z2)

COUPLED OSCILLATORS There are two balls which have mass m. One of the balls is attached to a ceiling by a spring and the other ball is attached to the first ball with another spring, and hangs below Ball 1 as shown in the figure. The two springs have spring constant k, and an equilibrium length a. Motions in the z direction are the ones considered, and the gravitation force (of constant acceleration g) points in the negative z-axis. Contact interactions between the balls can be ignored. (i) For such a scenario, provide the equations of motion (ii) Provide the rest positions. iii) Finally, calculate the oscillation frequencies and give the general solutions to this problem (z1,z2)

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COUPLED OSCILLATORS There are two balls which have mass m. One of the balls is attached to a ceiling by a spring and the other ball is attached to the first ball with another spring, and hangs below Ball 1 as shown in the figure. The two springs have spring constant k, and an equilibrium length a. Motions in the z direction are the ones considered, and the gravitation force (of constant acceleration g) points in the negative z-axis. Contact interactions between the balls can be ignored. (i) For such a scenario, provide the equations of motion (ii) Provide the rest positions. iii) Finally, calculate the oscillation frequencies and give the general solutions to this problem (z1,z2) Z mg k m 0 Z1 Z2
Transcribed Image Text:COUPLED OSCILLATORS There are two balls which have mass m. One of the balls is attached to a ceiling by a spring and the other ball is attached to the first ball with another spring, and hangs below Ball 1 as shown in the figure. The two springs have spring constant k, and an equilibrium length a. Motions in the z direction are the ones considered, and the gravitation force (of constant acceleration g) points in the negative z-axis. Contact interactions between the balls can be ignored. (i) For such a scenario, provide the equations of motion (ii) Provide the rest positions. iii) Finally, calculate the oscillation frequencies and give the general solutions to this problem (z1,z2) Z mg k m 0 Z1 Z2
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