Simple Harmonic Motion (SHM) Calculator
Calculator
Calculate SHM period, frequency, and maximum velocity from mass, spring constant, and amplitude.
Results
Data Source and Methodology
The calculations are based on standard physics equations for Simple Harmonic Motion (SHM) derived from Hooke's Law and Newton's Second Law of Motion.
The Formula Explained
Period \( T = 2\pi \sqrt{\frac{m}{k}} \)
Frequency \( f = \frac{1}{T} \)
Maximum Velocity \( v_{max} = A \cdot \omega \)
Where \( \omega = \sqrt{\frac{k}{m}} \)
Glossary of Variables
- Mass (m): The mass attached to the spring (kg).
- Spring Constant (k): The stiffness of the spring (N/m).
- Amplitude (A): The maximum displacement from equilibrium (m).
How It Works: A Step-by-Step Example
Consider a mass of 0.5 kg and a spring constant of 200 N/m with an amplitude of 0.2 m:
1. Calculate the angular frequency \( \omega = \sqrt{\frac{200}{0.5}} = 20 \, rad/s \)
2. Calculate the period \( T = 2\pi \sqrt{\frac{0.5}{200}} \approx 0.314 \, s \)
3. Calculate the frequency \( f = \frac{1}{0.314} \approx 3.18 \, Hz \)
4. Calculate the maximum velocity \( v_{max} = 0.2 \times 20 = 4 \, m/s \)
Frequently Asked Questions (FAQ)
What is Simple Harmonic Motion?
Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement.
How is the period of SHM calculated?
The period \( T \) is calculated using the formula \( T = 2\pi \sqrt{\frac{m}{k}} \).
What affects the frequency of SHM?
The frequency depends on the mass and the spring constant of the system.
What is the maximum velocity in SHM?
The maximum velocity occurs when the object passes through the equilibrium position.
Can SHM occur in systems other than springs?
Yes, SHM can occur in pendulums and other systems where the restoring force is proportional to displacement.
Formula (LaTeX) + variables + units
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Period \( T = 2\pi \sqrt{\frac{m}{k}} \)
Frequency \( f = \frac{1}{T} \)
Maximum Velocity \( v_{max} = A \cdot \omega \)
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Last code update: 2026-01-19
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