A Lightly Damped Harmonic Oscillator, with a Damping Force Proportional

question 2

Multiple Choice

A lightly damped harmonic oscillator, with a damping force proportional to its speed, is oscillating with an amplitude of 0.500 cm at time t = 0. When t = 8.20 s, the amplitude has died down to 0.400 cm. At what value of t will the oscillations have an amplitude of 0.250 cm?

• A) 18.5 s
• B) 20.5 s
• C) 16.5 s
• D) 25.5 s
• E) 5.13 s

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Definitions:

Radical

Refers to the root of a number, with the most common being the square root, though it can refer to cube roots or higher.

Square Root

A number which produces a specified quantity when multiplied by itself.

Square Root

The figure that, upon being multiplied with itself, results in the starting number.

Radial Approximation

A method or process used to estimate values or functions based on their radial distance from a central point.