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## A mass m=4kg is attached to both a spring with spring constant k=577N/m and a dash-pot with damping constant c=4N⋅s/m . The mass is started

Question

A mass m=4kg is attached to both a spring with spring constant k=577N/m and a dash-pot with damping constant c=4N⋅s/m . The mass is started in motion with initial position x0=5m and initial velocity v0=7m/s . Determine the position function x(t) in meters.

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Physics
3 years
2021-08-25T03:51:04+00:00
2021-08-25T03:51:04+00:00 1 Answers
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## Answers ( )

Answer:Explanation:The position and velocity functions have the following forms:

Where:

First, the angular frequency of oscillation is calculated:

Later, it is needed to determine if system is underdamped, critically damped or overdamped. Critic value is given by . The value is:

As c is lower than α, the system has an underdamped behavior. The initial values for position and velocity are, respectively:

Then,

By making some algebraic handling:

The amplitude is:

The position function is: