Question

oscillating spring mass systems can be used to experimentally determine an unknown mass without using a mass balance. a student observes that a particular spring-mass system has a frequency of oscillation of 10 Hz. the spring constant of the spring is 250 N/m. what is the mass?​

Answer 1

Answer:

0.063 Kg

Explanation:

From the question given above, the following data were obtained:

Frequency (f) = 10 Hz

Spring constant (K) = 250 N/m

Mass (m) =?

Next, we shall determine the period of oscillation. This can be obtained as follow:

Frequency (f) = 10 Hz

Period (T) =?

T = 1/f

T = 1/10

T = 0.1 s

Finally, we shall determine the mass of the spring. This can be obtained as follow:

Spring constant (K) = 250 N/m

Period (T) = 0.1 s

Pi (π) = 3.14

Mass (m) =?

T = 2π√(m/K)

0.1 = 2 × 3.14 × √(m/250)

0.1 = 6.28 × √(m/250)

Divide both side by 6.28

0.1 / 6.28 = √(m/250)

Take the square of both side.

(0.1 / 6.28)² = m/250

Cross multiply

m = (0.1 / 6.28)² × 250

m = 0.063 Kg

Therefore, the mass of the spring is 0.063 Kg.