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

question 17

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 $F ( t ) = 6 F _ { 0 } \cos ( \omega t )$ 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)\(x ( t ) = c _ { 1 } \cos ( \omega t ) + c _ { 2 } \sin ( \omega t ) + \frac { F _ { 0 } t ^ { - 2 } } { 2 M \omega } \sin ( \omega t )\)
• C)\(x ( t ) = c _ { 1 } \cos ( \omega t ) + c _ { 2 } \sin ( \omega t ) + \frac { 3 F _ { 0 } t } { M \omega } \sin ( \omega t )\)
• D)\(x ( t ) = \frac { F _ { 0 } t } { 2 M \omega } \left( c _ { 1 } \cos ( \omega t ) + c _ { 2 } \sin ( \omega t ) \right)\)
• E)\(x ( t ) = \frac { F _ { 0 } t ^ { 2 } } { 2 M \omega } \cos ( \omega t )\)

Understand the function of regulatory T cells (Tregs) in maintaining immune tolerance.

Detail the initial steps in the inflammatory response to injury or infection.

Analyze strategies for immunosuppression and the reasoning behind vaccine effectiveness.

Understand different modes of reproduction in animals, including sexual and asexual methods.

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