Question

A mass on a spring oscillates with a frequency of 0.1 hz. the mass is 10 kg. what is the spring constant of the spring?

a. 40 n/m
b. 4000 n/m
c. 4 n/m
d. 40,000 n/m

Answer 1

To find the spring constant (k) of a spring with a known mass (m) and frequency (f), use the formula k = (2πf)² ∙ m. Plugging in f = 0.1 Hz and m = 10 kg, we find that the spring constant is approximately 4 N/m, which is option c.

Step-by-step explanation:

The question is looking to find the spring constant of a spring when the mass and frequency of oscillation are known. The formula for the frequency (f) of a mass (m) on a spring with spring constant (k) in simple harmonic motion is given by:

f = (1/2π) ∙ √(k/m)

By rearranging this formula to solve for the spring constant (k), we get:

k = (2πf)² ∙ m

Using the provided data: f = 0.1 Hz and m = 10 kg, the calculation would be:

k = (2π ∙ 0.1 Hz)² ∙ 10 kg

k = (0.6283)^2 ∙ 10 kg

k = 0.3947 ∙ 10 kg

k ≈ 4 N/m

So, the spring constant of the spring is 4 N/m, which corresponds to option c.