# A 200 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x = 5.0 cm and has vx = -30 cm/s. Determine the k.

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We know that the angular frequency can be expressed in different forms.

`omega = (2*pi)/(T)`

`omega = 2*pi*F`

`omega = sqrt(k/m)`

By equating 1 and 3 we can solve for the spring constant.

`sqrt(k/m) =(2*pi*F)`

where:

- k = spring constant (?)
- m = mass of the object = 200 g or 0.200 kg
- F = frequency = 2.0 Hz

`sqrt(k/m) =(2*pi*F)`

`(k/m) =(2*pi*F)^2`

`k =(2*pi*F)^2 * m`

`k = (2*pi*2.0)^2 * 0.2`

**k = 31.6 -> answer**

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