What is the relationship between the period of a simple harmonic oscillator and

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Question: What is the relationship between the period of a simple harmonic oscillator and its mass and spring constant?

Options:

Correct Answer: T = 2π√(m/k)

Solution:

The period T of a mass-spring system is given by T = 2π√(m/k).

What is the relationship between the period of a simple harmonic oscillator and its mass and spring constant?

What is the relationship between the period of a simple harmonic oscillator and its mass and spring constant?

Step 1: Understand what a simple harmonic oscillator is. It is a system that moves back and forth in a regular pattern, like a mass attached to a spring.
Step 2: Identify the two important factors in the formula: mass (m) and spring constant (k). The mass is how heavy the object is, and the spring constant measures how stiff the spring is.
Step 3: Learn the formula for the period (T) of the oscillator: T = 2π√(m/k). This means the period depends on both the mass and the spring constant.
Step 4: Notice that if the mass (m) increases, the period (T) also increases. This means it takes longer for the system to complete one full cycle.
Step 5: Observe that if the spring constant (k) increases, the period (T) decreases. A stiffer spring makes the system oscillate faster.
Step 6: Conclude that the period of a simple harmonic oscillator is directly related to the mass and inversely related to the spring constant.

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