Will the period of oscillation of the weight on the spring change if the iron weight is replaced

Will the period of oscillation of the weight on the spring change if the iron weight is replaced with an aluminum one of the same size?

1. Let’s write down the expression to determine the period of oscillation of the load on the spring:
T = 2π * √ (m / k), where m is the mass of the load, k is a coefficient showing the stiffness of the spring.
2. Let us write down the formula for determining the mass, through the density:
m = ρ * V
According to the reference book, we determine the density of substances:
ρzh = 7800 kg / m³
ρа = 2700 kg / m³
3. Substitute the mass in the formula for determining the period:
T = 2π * √ (m / k) = 2π * √ (ρ * V / k)
For an iron load, taking into account that the elasticity of the spring and the volume of the load do not change:
Tzh = 2π * √ (ρl * V / k)
For aluminum cargo:
Ta = 2π * √ (ρa * V / k)
4. Divide Tzh / Tа:
Tl / Ta = (2π * √ (ρl * V / k)) / (2π * √ (ρa * V / k)
5. Substitute the numerical values:
Tzh / Ta = √7800 / √2700 = 88.31 / 51.96 = 1.7
Answer: the oscillation period will change 1.7 times.