Question

If the spring constant is doubled, how does the period of a mass on a spring change?

a. The period would change by a factor of 2.
b. The period would change by a factor of 1/2.
c. The period would change by a factor of 4.
d. The period would change by a factor of 1/4.

Answer 1

Doubling the spring constant would lead to the period of a mass-spring harmonic oscillator changing by a factor of 1/2 since the period is inversely proportional to the square root of the spring constant.

Step-by-step explanation:

If the spring constant of a simple harmonic oscillator is doubled, the period of the mass-spring system will change inversely proportional to the square root of the spring constant. Specifically, if the spring constant (k) is doubled, the new period (T') can be found using the formula for the period of a mass-spring system, which is T = 2π√(m/k) where m is the mass and k is the spring constant. To keep the frequency the same when k is doubled, the mass would need to be quadrupled because the period is proportional to the square root of the mass. Therefore, the correct answer is that the period would change by a factor of 1/2, which corresponds to option b.