Answer: the period of oscillation of the spring-mass system is 0.903 seconds, and its frequency is 1.77 Hertz.
Step-by-step explanation/works/how to solve:
To find the period of oscillation and frequency of the spring-mass system, we can use the following formulas:
Period of oscillation = 2π√(m/k)
Frequency = 1/(2π) * √(k/m)
Where m is the mass attached to the spring, k is the spring constant, and π is a mathematical constant approximately equal to 3.14159.
Using the given information, we can first find the spring constant k:
k = (mg)/(δx)
where g is the acceleration due to gravity (9.8 m/s²), δx is the change in length of the spring (0.04 m), and m is the mass attached to the spring (0.2 kg).
Plugging in the values, we get:
k = (0.2 kg * 9.8 m/s²)/(0.04 m) = 49 N/m
Now we can use this value of k to find the period of oscillation:
T = 2π√(m/k) = 2π√(0.2 kg/49 N/m) = 0.903 s (to three significant figures)
And the frequency:
f = 1/(2π) * √(k/m) = 1/(2π) * √(49 N/m / 0.2 kg) = 1.77 Hz (to three significant figures)