AP Physics 1
7.4 Energy of Simple Harmonic Oscillators
3.4 Conservation of Energy
Multi-Unit
Four independent horizontal spring-mass systems oscillate in simple harmonic motion on a frictionless surface. Each system consists of an ideal spring and a block, with parameters given in the table. Position x = 0 represents the equilibrium position for each system.
Which of the following correctly ranks the speeds \(v_1\), \(v_2\), \(v_3\), and \(v_4\) of the blocks at their respective positions of interest?
| System | Block mass | Spring constant | Amplitude | Position of interest |
|---|---|---|---|---|
| 1 | \(m\) | \(k\) | \(A\) | \(x = 0\) |
| 2 | \(m\) | \(2k\) | \(A\) | \(x = \dfrac{\sqrt{2}}{2}A\) |
| 3 | \(2m\) | \(8k\) | \(A\) | \(x = \dfrac{1}{2}A\) |
| 4 | \(4m\) | \(k\) | \(2A\) | \(x = A\) |
Which of the following correctly ranks the speeds \(v_1\), \(v_2\), \(v_3\), and \(v_4\) of the blocks at their respective positions of interest?
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