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

question 148

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

Analyze the role of social, cultural, and psychological factors in shaping individual and group decisions.

Understand the historical and current research methods and outcomes in the study of social influence, including key experiments.

Discuss the implications of online environments on social influence and group dynamics.

Critically evaluate real-life scenarios of social influence and propose strategies for negotiation and decision-making.

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