A mass of 0.5 kg is attached to a spring with a spring constant of 200 N/m. What

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Question: A mass of 0.5 kg is attached to a spring with a spring constant of 200 N/m. What is the frequency of oscillation? (2021)

Options:

Correct Answer: 2 Hz

Exam Year: 2021

Solution:

The frequency f of a mass-spring system is given by f = (1/2π)√(k/m). Here, f = (1/2π)√(200/0.5) ≈ 2 Hz.

A mass of 0.5 kg is attached to a spring with a spring constant of 200 N/m. What is the frequency of oscillation? (2021)

A mass of 0.5 kg is attached to a spring with a spring constant of 200 N/m. What is the frequency of oscillation? (2021)

Step 1: Identify the mass (m) and the spring constant (k). Here, m = 0.5 kg and k = 200 N/m.
Step 2: Write down the formula for the frequency (f) of a mass-spring system: f = (1/2π)√(k/m).
Step 3: Substitute the values of k and m into the formula: f = (1/2π)√(200/0.5).
Step 4: Calculate the value of k/m: 200 / 0.5 = 400.
Step 5: Take the square root of 400: √400 = 20.
Step 6: Multiply by (1/2π): f = (1/2π) * 20.
Step 7: Calculate (1/2π) * 20: f ≈ 3.18 Hz.
Step 8: Round the answer to the nearest whole number if needed: f ≈ 3 Hz.

Simple Harmonic Motion – The question tests understanding of the frequency of oscillation in a mass-spring system, which is a fundamental concept in mechanics.
Spring Constant and Mass Relationship – It assesses the relationship between the spring constant (k) and the mass (m) in determining the frequency of oscillation.