Suppose a Spring Has Mass M and Spring Constant K $$\omega = \sqrt { k / M }$$

question 6

Multiple Choice

Suppose a spring has mass M and spring constant k and let $$\omega = \sqrt { k / M }$$ . Suppose that the damping constant is so small that the damping force is negligible. If an external force $F ( t ) = 8 F _ { 0 } \cos ( \omega t )$ is applied (the applied frequency equals the natural frequency) , use the method of undetermined coefficients to find the equation that describes the motion of the mass.

• A) \(x ( t ) = c _ { 1 } \cos ( \omega t ) + c _ { 2 } \sin ( \omega t ) + \frac { F _ { 0 } t ^ { - 2 } } { 2 M \omega } \sin ( \omega t )\)
• B) \(x ( t ) = c _ { 1 } \cos ( \omega t ) + c _ { 2 } \sin ( \omega t ) + \frac { F _ { 0 } e ^ { - \omega t } } { 2 M \omega }\)
• C) \(x ( t ) = c _ { 1 } \cos ( \omega t ) + c _ { 2 } \sin ( \omega t ) + \frac { 4 F _ { 0 } t } { M \omega } \sin ( \omega t )\)
• D) \(x ( t ) = \frac { F _ { 0 } t ^ { 2 } } { 2 M \omega } \cos ( \omega t )\)
• E) \(x ( t ) = \frac { F _ { 0 } t } { 2 M \omega } \left( c _ { 1 } \cos ( \omega t ) + c _ { 2 } \sin ( \omega t ) \right)\)

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Definitions:

Collective Unconscious

A concept in psychology referring to the part of the unconscious mind which is derived from ancestral memory and experience and is common to all humankind.

Archetypes

Symbolic, universally recognized characters or themes that recur across different cultures and literature, as identified in Jungian psychology.

Primary Attitudes

Fundamental feelings or beliefs that are held by an individual toward objects, people, or concepts.

Ego

Within the framework of psychoanalytic theory, it is the component of personality responsible for balancing the needs of the id, superego, and the external world.