A 5.0 kg object suspended on a spring oscillates such that its position x as a function of time t is given by the equation x (t ) = A cos(ωt ), where A = 0.80 m and ω = 2.0 s-1 . What is the magnitude of the maximum net force on the object during the motion?

The magnitude of the maximum net force on the object during the motion is 16 newtons.

Explanation:

The position of the mass, measured in meters, within the mass-spring system is:

(1)

Where:

- Amplitude, measured in meters.

- Time, measured in seconds.

- Angular frequency, measured in radians per second.

The acceleration function (), measured in meters per square second, is obtained by deriving twice (1) in time:

(2)

And the maximum acceleration (), measured in meters per square second, experimented by the mass is:

(3)

And the maximum net force (), measured in newtons, is:

(4)

If we know that , and , then the maximum net force on the object during the motion is:

The magnitude of the maximum net force on the object during the motion is 16 newtons.

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