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Moving mass m collides with stationary mass M attached to a spring on a frictionless table. Write SHM equations.

SEE ATTACHMENT #1 for a diagram of parameters and a reference circle.

On a horizontal, frictionless table, a mass M is attached to the free end of a spring with the other end fixed. Another mass, m, moving at velocity S, collides and sticks to mass M and at that point, SHM begins. The spring's force constant is k.

PART a. In terms of given parameters, write (1) x(t), (2) v(t) and (3) a(t).

PART b. Given values are: M= 4.32 kg, m= 1.44 kg, S= 2.4 m/sec, k= 64 nt/m.
Calculate the following for the moving combined mass:
initial velocity vo, angular frequency (omega); Period T; amplitude xm; position x at t= .6 sec; velocity v at t= 1.5 sec.


Solution Preview

See attached file.

Solution with explanations:

General SHM with initial phase angle.

On ATTACHMENT #2, the upper diagrams show the basic equation x(t) of any SHM is in terms of the constants; amplitude xm, angular frequency (omega), and the initial phase angle (theta). The reference circle is a helpful device in finding x(t).

PART a. For this problem, the lower diagrams in ATTACHMENT #2 show the apparatus and a reference circle relating to the given ...

Solution Summary

With good explanation and calculations, the answers to the problems are solved.