An oscillator of mass m = 2 kg, whose natural frequency of oscillation is 10 rad

Question

An oscillator of mass m = 2 kg, whose natural frequency of oscillation is 10 radians/s , feels a force when the oscillator is in motion,
F = -k x - m? d x/dt.
What is the value of the spring constant k?

1. 50 N/m
2. 150 N/m
3. 100 N/m
4. 250 N/m
5. 200 N/

At what value of ? will the damping rate of
the spring be ?/2, without any oscillations of
the spring?
1. 50 s^-1
2. 40 s^-1
3. 20 s^-1
4. 10 s^-1
5. 30 s^-1

I am fairly lost on this problem, so as much explanation as possible would be greatly appreciated.

Explanation / Answer

For the fist part of you question, the equation for the natural frequency of a spring mass system is equal to sqrt(k/m). Knowing this the equation becomes 10^2 = k/2 therefor k is equal to 200N/m The second part of your question I do not understand. What is the "?" supposed to be?

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