To find the period of the oscillation, we can use Hooke's Law and the formula for the period of a mass-spring system. Here's how to do it:
1. Start by calculating the spring constant, denoted by 'k'. According to Hooke's Law, the force exerted by a spring is proportional to its displacement. In this case, with a 10g mass stretching the spring by 3.90 cm (which is 0.039 m), we can write the equation as follows:
F = -k * x
Where F is the force applied by the mass, k is the spring constant, and x is the displacement of the spring.
Since the force applied is the weight of the mass (10g), we can convert it to Newtons using the equation:
Force = mass * acceleration due to gravity
Mass = 10g = 0.01 kg (given that 1 kg = 1000 g)
Acceleration due to gravity (g) = 9.8 m/s^2
Plugging these values into the equation:
Force = 0.01 kg * 9.8 m/s^2 = 0.098 N
Therefore:
0.098 N = -k * 0.039 m
2. Rearrange the equation to solve for 'k':
k = -0.098 N / 0.039 m ≈ -2.513 N/m
The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement.
3. Now we can use the formula for the period of a mass-spring system:
T = 2Ï€ * sqrt(m / k)
Where T is the period of the oscillation, m is the mass attached to the spring, and k is the spring constant.
Plugging in the values:
m = 25g = 0.025 kg
T = 2Ï€ * sqrt(0.025 kg / -2.513 N/m)
Performing the calculations:
T ≈ 2 * 3.14159 * sqrt(0.025 kg / -2.513 N/m)
T ≈ 2 * 3.14159 * sqrt(0.009952 kg/m)
T ≈ 2 * 3.14159 * 0.09976 s ≈ 0.626 s
Therefore, the period of the oscillation is approximately 0.626 seconds.