A simple harmonic oscillator has a mass of 2 kg and a spring constant of 50 N/m.

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Question: A simple harmonic oscillator has a mass of 2 kg and a spring constant of 50 N/m. What is the angular frequency of the oscillator?

Options:

Correct Answer: 10 rad/s

Solution:

The angular frequency ω is given by the formula ω = √(k/m). Here, k = 50 N/m and m = 2 kg. Thus, ω = √(50/2) = √25 = 5 rad/s.

A simple harmonic oscillator has a mass of 2 kg and a spring constant of 50 N/m. What is the angular frequency of the oscillator?

A simple harmonic oscillator has a mass of 2 kg and a spring constant of 50 N/m. What is the angular frequency of the oscillator?

Step 1: Identify the mass (m) of the oscillator, which is given as 2 kg.
Step 2: Identify the spring constant (k) of the oscillator, which is given as 50 N/m.
Step 3: Write down the formula for angular frequency (ω), which is ω = √(k/m).
Step 4: Substitute the values of k and m into the formula: ω = √(50/2).
Step 5: Calculate the value inside the square root: 50 divided by 2 equals 25.
Step 6: Take the square root of 25, which equals 5.
Step 7: Conclude that the angular frequency (ω) is 5 rad/s.

Simple Harmonic Motion – The study of oscillatory motion where the restoring force is proportional to the displacement from equilibrium.
Angular Frequency – A measure of how quickly an object oscillates, calculated using the formula ω = √(k/m).
Spring Constant – A measure of the stiffness of a spring, represented by k in Hooke's law.