In a simple harmonic oscillator, if the mass is increased while keeping the spri

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Question: In a simple harmonic oscillator, if the mass is increased while keeping the spring constant the same, what happens to the period?

Options:

Correct Answer: Increases

Solution:

The period T = 2π√(m/k) increases with an increase in mass (m).

In a simple harmonic oscillator, if the mass is increased while keeping the spring constant the same, what happens to the period?

In a simple harmonic oscillator, if the mass is increased while keeping the spring constant the same, what happens to the period?

Step 1: Understand what a simple harmonic oscillator is. It consists of a mass attached to a spring that moves back and forth.
Step 2: Know the formula for the period (T) of a simple harmonic oscillator: T = 2π√(m/k), where m is the mass and k is the spring constant.
Step 3: Identify that in this question, the spring constant (k) remains the same while the mass (m) is increased.
Step 4: Recognize that increasing the mass (m) will affect the value inside the square root in the formula.
Step 5: Realize that as mass (m) increases, the value of √(m/k) also increases because k is constant.
Step 6: Conclude that since T is directly proportional to √(m/k), an increase in mass (m) will lead to an increase in the period (T).

Simple Harmonic Motion – The behavior of systems that exhibit periodic motion, such as mass-spring systems.
Period of Oscillation – The time taken for one complete cycle of motion, which depends on mass and spring constant.
Effect of Mass on Period – Increasing mass in a simple harmonic oscillator increases the period of oscillation.