ASVAB (Armed Services Vocational Aptitude Battery)Mechanical Comprehension (MC)Medium
A technician is observing a simple harmonic motion system, specifically a mass attached to a spring. Which statement accurately describes the relationship between the mass, spring constant, and the period of oscillation?
- AIncreasing the mass will increase the period of oscillation.
- BDecreasing the spring constant will decrease the period of oscillation.
- CIncreasing the mass will decrease the period of oscillation.
- DThe period of oscillation is independent of the mass and spring constant.
Show answer & explanationAnswer & explanation
Correct answer: A. Increasing the mass will increase the period of oscillation.
The period (T) of a mass-spring system is given by T = 2π√(m/k), where 'm' is mass and 'k' is the spring constant. From this formula, it's clear that increasing the mass (m) will increase the period (T), meaning it takes longer to complete one oscillation.
Why the other options are wrong
- B. This is incorrect; decreasing the spring constant (weaker spring) makes the oscillation slower, thus increasing the period.
- C. This is incorrect; increasing mass makes the oscillation slower, thus increasing the period.
- D. This is incorrect; both mass and spring constant are fundamental determinants of the period of oscillation.
Mass-Spring Period
The time it takes for a mass attached to a spring to complete one full oscillation. It depends on the mass (m) and the spring constant (k), described by the formula T = 2π√(m/k).
- Period increases with increasing mass.
- Period increases with decreasing spring constant (weaker spring).
- Amplitude of oscillation does not affect the period.
Memory trick: Heavy 'mass' needs 'more time' to 'spring' back.