If the mass attached to a spring is increased and the constant is decreased, does the period of the oscillating motion increase, decrease or stay the same

Increase

Explanation:

The period of an oscillating system is the time it takes for the system to complete 1 oscillation.

The period of a spring-mass oscillating system is given by

where

k is the spring constant

m is the mass

We see that:

- The period is proportional to the square root of the mass: so as the mass increases, the period increases too (1)

- The period is inversely proportional to the square root of the spring constant: so as the constant decreases, the period increases (2)

In this problem:

- The mass of the system is increased

- The spring constant is decreased

Therefore, according to observations (1) and (2), the period of the system will increase.

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