Physics Demonstrations

Spring Mass

Mass (kg)
Spring Constant (N/m)
Initial Displacement (m)

In this demonstration, we explore the oscillation of a mass ( $m$ ) attached to a spring with spring constant ( $k$ ), displaced an initial distance ( $A$ ) from its equilibrium position. By Hooke's Law, the restoring force on the mass is: $F = - k \cdot x$ Applying Newton's second law gives the equation of motion: $m \cdot \ddot{x} = - k \cdot x$ The solution describes simple harmonic motion: $x (t) = A \cdot \cos (ω \cdot t)$ Where the angular frequency and period are: $ω = \sqrt{\frac{k}{m}} T = \frac{2 π}{ω} = 2 π \sqrt{\frac{m}{k}}$ Some questions to consider while viewing the demonstration: How does increasing the mass affect the period of oscillation? How does increasing the spring constant affect it? The amplitude $A$ does not appear in the formula for $T$ . What does this tell you about the relationship between amplitude and period? Identify a real-world system that behaves like a spring-mass oscillator.