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

question 38

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

Identify the effect of psychological interventions, like the placebo effect, on pain and immune response.

Distinguish between optimistic and pessimistic explanatory styles and their impact on health.

Recognize the influence of personal control and lifestyle choices on health and stress management.

Understand the complex relationship between stress exposure and physical health, factoring in immunity, heredity, and environmental factors.

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Definitions:

Discrepancies

Differences or inconsistencies between two or more facts, figures, opinions, or outcomes.

Self-Esteem

An individual's subjective evaluation of their own worth, encompassing beliefs and emotions about oneself.

Violence

The use of physical force with the intent to harm, damage, or kill someone or something.

Self-Motive

The internal drive that propels individuals to pursue goals, make decisions, and engage in behaviors that fulfill their personal desires and needs.