Answer:
The frequency of the system can be found using the formula:
f = 1 / (2π) * sqrt(k / m)
where f is the frequency, k is the spring constant, and m is the mass.
For the given system, with a mass of 10 kg and a spring constant of 20 N/m, the frequency is:
f = 1 / (2π) * sqrt(20 N/m / 10 kg) = 0.79 Hz
If the system is held vertically, the force of gravity will act on the mass, which will change the equilibrium position of the spring. The new equilibrium position will be lower than the original position, so the mass will be displaced by a greater distance before the spring exerts a restoring force.
To find the new frequency, we can use the formula:
f = 1 / (2π) * sqrt((k/m) - (g/L))
where g is the acceleration due to gravity and L is the length of the spring when it is at rest.
Assuming that the length of the spring remains constant, the new frequency can be calculated as:
f = 1 / (2π) * sqrt((20 N/m / 10 kg) - (9.81 m/s^2 / 0.1 m)) = 0.70 Hz
So the frequency of the system is slightly lower when it is held vertically due to the effect of gravity on the equilibrium position of the spring.