You walk into a room and notice that there someone is running an experiment involving a...

You walk into a room and notice that there someone is running an experiment involving a spring-mass system. You have no idea when the experiment started, but observe that the mass attached to the spring is oscillating with period 3 (seconds) and that the amplitude of the oscillations remain constant (to your naked eye) while you are in the room. What are two differential equations which model the motion of the mass? One system must be inhomogeneous and the other must be homogeneous. Do not worry about the initial conditions.

Expert Solution

There can be any of the two types of situations or systems I can observe. The object with mass m attached with the spring can be oscillating either verically or horizontally. Let us consider each of the two cases. This is the second order inhomogenious equation due to a damping force. This equation will be same for a mass attached with spring vibrating vertically if we consider air friction is acting against the motion. In this case the air frictional force will act as damping force and will give rise to the same differential equation.

genius_generous answered 2 months ago

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