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)\(x ( t ) = \frac { F _ { 0 } t ^ { 2 } } { 2 M \omega } \cos ( \omega t )\)

---

Definitions:

Decision Rules

Guidelines or criteria used to make choices between alternatives in decision-making processes.

Performance Opportunity

refers to situations or conditions that allow an individual or organization to perform tasks or activities effectively, enhancing overall performance.

Actual Situation

The real and present condition or state of affairs, without any alterations or embellishments.

Better Than Anticipated

Results or outcomes that surpass the expected or forecasted standards.