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Object of mass 2M moving with SHM: Find period, velocity, amplitude

SEE ATTACHMENT #1 for diagram showing parameters, and general equations of SHM.

Driven by a spring with force constant k, on a horizontal frictionless table, two joined masses, each mass M, is executing SHM between xm and -xm. Known parameter values are: M= 2 kg, k= 64 nt/m, xm= .25 m,

PART a. Find the period, and maximum velocity, with both masses executing SHM.
PART b. If one of the masses is detached at +xm, find the subsequent period, amplitude, and maximum velocity of the remaining mass.
PART c. If one of the masses is detached at the center, x=0, moving toward +xm, find the subsequent period, amplitude and maximum velocity of the remaining mass.

Attachments

Solution Preview

Step 1. Note the general equations shown on ATTACHMENT #1:

PART a.
For the original period, applying (6) should give you: T= .5 (PI) = 1.57 sec.
Then applying 'total KE at center = total PE at xm' should give you: Vo= 1 m/sec.

PART b.
If one mass is detached at +xm, where the system is ...

Solution Summary

The solution carefully explains each problem and provides the calculation for answers.

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