1. What is the Periodic Time of Mass Attached to Closely Coiled Helical Spring which is Hanged Vertically?

The periodic time refers to the time taken for one complete oscillation of a mass attached to a vertically hanging helical spring. This represents a simple harmonic motion system where the restoring force is proportional to the displacement from equilibrium position.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( T \) — Time period of oscillation (seconds)
• \( M \) — Mass of the body (kg)
• \( k \) — Stiffness of the spring (N/m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula shows that the time period is directly proportional to the square root of the mass and inversely proportional to the square root of the spring stiffness. This relationship is fundamental to simple harmonic motion systems.

3. Importance of Time Period Calculation

Details: Calculating the time period is crucial for understanding oscillatory systems, designing mechanical systems with specific vibration characteristics, and analyzing the dynamic behavior of spring-mass systems in various engineering applications.

4. Using the Calculator

Tips: Enter the mass in kilograms and spring stiffness in Newtons per meter. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect the time period of oscillation?
A: The time period depends only on the mass attached to the spring and the spring stiffness. It is independent of the amplitude of oscillation for small displacements.

Q2: Does gravity affect the time period calculation?
A: No, gravity affects the equilibrium position but not the time period of oscillation for a spring-mass system.

Q3: What are typical values for spring stiffness?
A: Spring stiffness values vary widely depending on the application, ranging from very soft springs (few N/m) to very stiff springs (thousands of N/m).

Q4: Is this formula valid for all types of springs?
A: This formula applies specifically to closely coiled helical springs that obey Hooke's law, where the restoring force is proportional to displacement.

Q5: How does mass distribution affect the time period?
A: For a point mass attached to a massless spring, the formula is exact. For springs with significant mass, additional corrections may be needed.