A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm. If the mass of the object is 0.20 kg, what is the spring constant

The spring has a constant of 126.334 newtons per meter.

Explanation:

Given that mass-spring system experiment a simple harmonic motion, the angular frequency of the system as a function of frequency is:

Where:

- Angular frequency, measured in radians per second.

- Frequency, measured in hertz.

Given that , the angular frequency of the system is:

Now, the angular frequency can be obtained in terms of spring constant and mass. That is:

Where:

- Spring constant, measured in newtons per meter.

- Mass, measured in kilograms.

The spring constant is now cleared:

If and , the spring constant is:

The spring has a constant of 126.334 newtons per meter.

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