10. A block is attached to a horizontal spring and slides back and forth on a fr

Question

10. A block is attached to a horizontal spring and slides back and forth on a frictionless horizontal surface. A second identical block is suddenly attached to the first block. The attachment is accomplished by joining the blocks at one extreme end of the oscillation cycle. The velocities of the blocks are exactly matched at the instant of joining. How do the (a) amplitude, (b) frequency, and (c) maximum speed of the simple harmonic motion change? Answer: The amplitude is unchanged. The frequency and maximum speed each decrease by a factor of . Explain.

Explanation / Answer

a) The amplitude depends only on the energy stored in the spring. This energy is constant and so the amplitude must also be constant. Nothing happens to the amplitude. b) Frequency = 1/T and T = 2p v m/k Bigger m means larger T an larger T means smaller frequency. . c) The maximum speed will be less - energy is fixed so when tis all KE, the greater mass will mean that the speed must be reduced.

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