This question requires Hooke's law to solve:
where F is the force in newtons used to displace the mass by x in metres; k is the spring constant. With the force used to displace the mass, we can know the spring constant.
Using the fact that
then it can be rearranged with Hooke's law to give
which can also be written as
The solutions to this equations take the form
where A and B are the amplitudes (maximum displacement) of the system and `omega` is the angular frequency. As x(0)=0, the first of the two equations is appropriate in this occasion.
To determine the angular frequency we need the time period of the oscillator. This is
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