A Mass M Hanging on a Spring with a Spring

question 109

Multiple Choice

A mass m hanging on a spring with a spring constant k executes simple harmonic motion with a period T. If the same mass is hung from a spring with a spring constant of 2k, the period of oscillation

• A) increases by a factor of 2.
• B) decreases by a factor of 2.
• C) increases by a factor of .
• D) decreases by a factor of .
• E) is not affected.

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Definitions:

Lagrange Multipliers

A strategy used in mathematical optimization to find the local maxima and minima of a function subject to equality constraints.

Constrained Optimization

The process of finding the maximum or minimum value of a function subject to certain constraints, common in economics to find the optimal resource allocation.

Cobb-Douglas

A form of production function that represents the relationship between two or more inputs (typically labor and capital) and the amount of output produced, characterized by constant returns to scale and substitution between inputs.

Constrained Optimization

The process of finding the optimal solution or outcomes within given limitations or constraints.