Question:
A mass of 1 kg is attached to a spring of force constant 100 N/m. Time period is:
A mass of 1 kg is attached to a spring of force constant 100 N/m. Time period is:
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The time period is independent of the amplitude of oscillation. Whether you pull the spring a little or a lot, as long as it stays within its elastic limit, the time taken for one full bounce remains the same.
Updated On: Jun 3, 2026
- 0.2\(\pi\) s
- 0.1\(\pi\) s
- 0.5\(\pi\) s
- 2\(\pi\) s
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The Correct Option is A
Solution and Explanation
Concept:
The time period of a mass-spring system undergoing Simple Harmonic Motion (SHM) is the time taken for the mass to complete one full oscillation. It depends on the inertia (mass) and the stiffness (force constant) of the system.
• Formula: \( T = 2\pi \sqrt{\frac{m}{k}} \)
• \( m \): Mass attached to the spring.
• \( k \): Force constant (spring constant).
Step 1: Identifying the given parameters.
Mass (\( m \)) = 1 kg
Force constant (\( k \)) = 100 N/m
Step 2: Substituting values into the time period formula.
\[ T = 2\pi \sqrt{\frac{1}{100}} \]
Step 3: Calculating the final value.
\[ T = 2\pi \left( \frac{1}{10} \right) \] \[ T = \frac{2\pi}{10} = 0.2\pi \text{ s} \]
• Formula: \( T = 2\pi \sqrt{\frac{m}{k}} \)
• \( m \): Mass attached to the spring.
• \( k \): Force constant (spring constant).
Step 1: Identifying the given parameters.
Mass (\( m \)) = 1 kg
Force constant (\( k \)) = 100 N/m
Step 2: Substituting values into the time period formula.
\[ T = 2\pi \sqrt{\frac{1}{100}} \]
Step 3: Calculating the final value.
\[ T = 2\pi \left( \frac{1}{10} \right) \] \[ T = \frac{2\pi}{10} = 0.2\pi \text{ s} \]
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