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Simple Harmonic Motion Equation:
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Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. It's a fundamental concept in physics that describes many natural oscillations.
The calculator uses the SHM angular frequency equation:
Where:
Explanation: The equation shows that the angular frequency of oscillation depends on the stiffness of the spring (k) and the mass (m) attached to it.
Details: Angular frequency determines how fast the object oscillates. It's related to the period (T) and frequency (f) of oscillation by \( \omega = 2\pi f = \frac{2\pi}{T} \).
Tips: Enter spring constant in N/m and mass in kg. Both values must be positive numbers. The calculator will compute the angular frequency in radians per second.
Q1: What are typical values for spring constant?
A: Spring constants vary widely depending on the spring material and dimensions, from a few N/m for very loose springs to thousands of N/m for stiff springs.
Q2: How does mass affect the angular frequency?
A: As mass increases, angular frequency decreases (oscillations become slower), following an inverse square root relationship.
Q3: What's the difference between angular frequency and regular frequency?
A: Angular frequency (ω) is measured in radians per second, while regular frequency (f) is in Hertz (oscillations per second). They're related by ω = 2πf.
Q4: Can this equation be used for pendulums?
A: No, this specific equation is for mass-spring systems. For simple pendulums, the equation is \( \omega = \sqrt{g/L} \), where g is gravity and L is length.
Q5: What if the spring has significant mass?
A: For springs with non-negligible mass, the effective mass is approximately the attached mass plus one-third of the spring's mass.