In a simple harmonic motion, if the mass is increased while keeping the spring c

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

Options:

Correct Answer: Increases

Solution:

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

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

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

Step 1: Understand that simple harmonic motion involves a mass attached to a spring.
Step 2: Know that the period (T) is the time it takes for one complete cycle of motion.
Step 3: Remember the formula for the period of a mass-spring system: T = 2π√(m/k), where m is the mass and k is the spring constant.
Step 4: Identify that if the mass (m) increases while the spring constant (k) stays the same, the value of m in the formula increases.
Step 5: Realize that as m increases, the square root of m (√m) also increases, which makes T larger.
Step 6: Conclude that the period (T) increases when the mass is increased.

Simple Harmonic Motion – The study of oscillatory motion where the restoring force is proportional to the displacement.
Period of Oscillation – The time taken for one complete cycle of motion, which depends on mass and spring constant in a mass-spring system.
Mass-Spring System – A system where a mass is attached to a spring, and its motion can be described by Hooke's law.