A 0.40 kg mass hangs on a spring with a spring constant of 12 N/m. The system oscillated with a constant amplitude of 12 cm. What is the maximum acceleration of the system

The maximum acceleration of the system is 359.970 centimeters per square second.

Explanation:

The motion of the mass-spring system is represented by the following formula:

Where:

- Position of the mass with respect to the equilibrium position, measured in centimeters.

- Amplitude of the mass-spring system, measured in centimeters.

- Angular frequency, measured in radians per second.

- Time, measured in seconds.

- Phase, measured in radians.

The acceleration experimented by the mass is obtained by deriving the position equation twice:

Where the maximum acceleration of the system is represented by .

The natural frequency of the mass-spring system is:

Where:

- Spring constant, measured in newtons per meter.

- Mass, measured in kilograms.

If and , the natural frequency is:

Lastly, the maximum acceleration of the system is:

The maximum acceleration of the system is 359.970 centimeters per square second.

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement