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.

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