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.

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:

battery with hi vtge high val resist in series