Energy in simple harmonic motion

Equipment

• Virtual mass–spring oscillator without friction
• Sliders “Biên độ A” (amplitude), “Khối lượng m” (mass), “Độ cứng k” (stiffness)
• Instantaneous energy bars: red for potential, blue for kinetic
• “Tạm dừng” (pause) button to freeze and read a state

Procedure

1. Watch the energy exchange

   Let the oscillator run and watch the red potential bar and the blue kinetic bar rise and fall out of phase. The vertical marker tracks the instantaneous state; notice that the total height of the bars stays constant, illustrating $E=K+U=\tfrac12kA^2$.

2. Check the energy at special points

   Press “Tạm dừng” when the mass passes equilibrium and again at maximum displacement. At $x=0$ all energy is kinetic, $K_{\max}=\tfrac12kA^2$; at $x=\pm A$ it is all potential. Read the bars and confirm $K=\tfrac12k(A^2-x^2)$ at an intermediate point.

3. Vary A, m and k

   Double the amplitude A and observe the total energy quadruple, since $E\propto A^2$. Then increase k at fixed A to raise E, and increase m: the total energy is unchanged, but the motion slows because the period $T=2\pi\sqrt{m/k}$ grows.

Simulation

Experiment history

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