Question

A 4.1 kg mass is connected to a spring with a spring constant of 5.3 N/m. The displacement is given by the expression x(t)=(3.64 cm)sin(ωt). What is the frequency of the simple harmonic motion?

Answer 1

The frequency of the simple harmonic motion for a mass attached to a spring with a constant of 5.3 N/m and mass of 4.1 kg is approximately 0.181 Hz.

Step-by-step explanation:

The frequency of the simple harmonic motion for a mass-spring system can be found using the formula for the angular frequency ω, which is given by ω = √(k/m), where k is the spring constant and m is the mass. The angular frequency is related to the frequency f by ω = 2πf. Thus, the frequency f can be calculated by rearranging the formula to f = ω/(2π).

For the given mass of 4.1 kg and spring constant of 5.3 N/m, the angular frequency ω can be calculated as:

• ω = √(k/m) = √(5.3 N/m / 4.1 kg) ≈ √(1.293 N/kg) ≈ 1.137 s-1

Now we can find the frequency f by dividing ω by 2π:

• f = ω/(2π) ≈ 1.137 s-1 / (2π) ≈ 0.181 Hz

Therefore, the frequency of the simple harmonic motion is approximately 0.181 Hz.