If the spring constant of a spring is doubled, how does the period of the simple

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Question: If the spring constant of a spring is doubled, how does the period of the simple harmonic motion change?

Options:

Correct Answer: It is halved

Solution:

The period T is inversely proportional to the square root of the spring constant k. If k is doubled, the period is halved.

If the spring constant of a spring is doubled, how does the period of the simple harmonic motion change?

If the spring constant of a spring is doubled, how does the period of the simple harmonic motion change?

Step 1: Understand that the period T of simple harmonic motion is related to the spring constant k.
Step 2: Know that the formula for the period T is T = 2π√(m/k), where m is the mass attached to the spring.
Step 3: Recognize that if the spring constant k is doubled, it becomes 2k.
Step 4: Substitute 2k into the formula: T = 2π√(m/(2k)).
Step 5: Simplify the equation: T = 2π√(m/k) * (1/√2).
Step 6: Notice that T is now T = (1/√2) * (2π√(m/k)), which means the period is reduced by a factor of √2.
Step 7: Conclude that if k is doubled, the period T is halved.

Simple Harmonic Motion – The relationship between the spring constant and the period of oscillation in a spring-mass system.
Period of Oscillation – The formula T = 2π√(m/k) shows that the period T is inversely proportional to the square root of the spring constant k.