To double the period of a simple harmonic oscillator, by what factor should the amplitude change?

Question

BlackTom AI · Accepted Answer

We are asked about how amplitude must change to double the period of a simple harmonic oscillator. The period T for an ideal SHM is T = 2π sqrt(m/k), which shows that T depends on mass m and spring constant k, but not on amplitude A. With that in mind, let's evaluate each option.

Option 1: none of these. Since the period does not depend on amplitude, changing the amplitude cannot double the period. The doubling of the period would require altering m or k (as in T ∝ sqrt(m/k)); therefore, this option correctly reflects that none of the listed amplitude factors will achieve the doubling.

Option 2: square root of 2. If the amplitude were to change by a factor of sqrt(2), the period would remain unaffected in an ideal SHM, because amplitude is not a factor in the T formula. Therefore this option is incorrect.

Option 3: two. Doubling the amplitude would not change the period in an ideal SHM. The velocity and energy scale with amplitude, but the period remains governed by mass and stiffness. Thus this option is incorrect.

Option 4: four. Similar reasoning to option 3: amplitude scaling does not alter the period, so quadrupling the amplitude does not double the period. This option is incorrect.

Option 5: one half. Reducing the amplitude by a factor of two does not affect the period either, so this option is incorrect.

In summary, the only way to double the period would be to change system parameters (mass or spring constant) rather than amplitude. The evaluation shows that none of the listed amplitude changes produce the required doubling, aligning with the fundamental T ∝ sqrt(m/k) relationship rather than any amplitude dependence.

2025 Fall PHYS 2205 TR 11:00 - 12:15 _ 89122 2205 Final Exam

To double the period of a simple harmonic oscillator, by what factor should the amplitude change?

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