Question

A 0.500-kg mass suspended from a spring oscillates with a period of 1.50 s. How much mass must be added to the object to change the period to 2.00 s?

a) 0.125 kg
b) 0.250 kg
c) 0.375 kg
d) 0.500 kg

Answer 1

To change the period of oscillation, the mass must be increased by approximately 0.250 kg.

Step-by-step explanation:

To calculate the amount of mass that must be added to change the period of oscillation, we use the formula:

T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant.

Given that the initial period is 1.50 s and the final period is 2.00 s, and the initial mass is 0.500 kg, we can rearrange the formula to solve for the final mass.

Plugging in the values, we have: 1.50 = 2π√(0.500/k) and 2.00 = 2π√((0.500 + x)/k), where x is the additional mass.

Simplifying and solving these equations, we find that x ≈ 0.250 kg.