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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. The period, velocity and amplitude is examined. The object of mass 2M moving with SHM are given.

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