Question

A 250 g block hangs from a spring with spring constant 13 N/m. At t=0s the block is 15 cm below the equilibrium point and moving upward with a speed of 98.0 cm/s.

What is the block's oscillation frequency?

Answer 1

To calculate the oscillation frequency of a 250 g block on a spring, convert the mass to kilograms and use the formula f = 1 / (2π) ∙ √(k / m), resulting in a frequency of about 1.44 Hz.

Step-by-step explanation:

The question involves determining the oscillation frequency of a 250 g block attached to a spring with a spring constant of 13 N/m, when the block is released from a position 15 cm below the equilibrium point and moving upward at a speed of 98.0 cm/s. Since this is a scenario of simple harmonic motion (SHM), the oscillation frequency can be calculated using the formula for the frequency of a mass-spring system, which is f = 1 / (2π) ∙ √(k / m), where k is the spring constant and m is the mass of the block.

Step-by-step calculation:

1. Convert the mass of the block from grams to kilograms: m = 250 g = 0.250 kg.
2. Substitute the values of the spring constant (k = 13 N/m) and the mass (m = 0.250 kg) into the frequency formula:
3. Calculate the frequency: f = 1 / (2π) ∙ √(13 / 0.250) ≈ 1.44 Hz.

The block's oscillation frequency is therefore approximately 1.44 Hz.