AP Physics C Mechanics 7.1 SHM Overview

Describe simple harmonic motion as repeated oscillation about equilibrium with a restoring force that depends on displacement and direction.

[Maximum number: 2]

Mech.2.
A block of mass 2 M rests on a horizontal, frictionless table and is attached to a relaxed spring, as shown in the figure above. The spring is nonlinear and exerts a force $F(x)=-B x^{3}$ , where B is a positive constant and x is the displacement from equilibrium for the spring. A block of mass 3 M and initial speed $v_{0}$ is moving to the left as shown.

Do the two blocks, which remain stuck together and attached to the spring, exhibit simple harmonic motion after the collision?

Yes No
Justify your answer.

Figure 1

Figure 2

2 points
For selecting the correct answer "No," with a reasonable attempt at a justification If the incorrect selection is made, no points are earned for the justification. If the correct answer is selected without any justification, the point is not earned for the selection.
For an indication that the spring does not apply a linear force and that simple 1 point harmonic motion is the resulting motion of a linear restoring force $\left(a=-\frac{k}{m} \Delta x\right)$
Example:
Because the blocks are sticking together and are attached to the spring, the spring will apply a restoring force to the blocks. However, because the restoring force exerted by a nonlinear spring is not proportional to the blocks' displacement from equilibrium, the blocks do not exhibit simple harmonic motion.

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Covered syllabus points

7.1 Defining Simple Harmonic Motion (SHM) question 1