The mass is increased by a factor of four. What is true about the period? Choose the best answer.

The period remains unchanged.

The period increases by a factor of four.

The period is halved.

The period doubles.

The period decreases by a factor of four.

Answer: The period doubles.

Explanation: this is a question on the relationship between the period (T) of a loaded spring and it mass (m), the formulae relating both quantities is given below.

T = 2π * √m/k

Where T = period, m = mass and k = spring constant.

By squaring both sides, we have

T² = 4π² * m/k

T² = (4π²/k) * m

The expression (4π²/k) is a constant, hence

T² = K * m ... This implies that square of period is proportional to mass.

Hence

(T1) ²/m1 = (T2) ²/m2

From the question, m2 = 4m1 and we are to find T2.

(T1) ²/m1 = (T2) ²/4m1

(T1) ² = (T2) ²/4

4 (T1) ² = (T2) ²

T2 = √4 (T1) ²

T2 = 2T1

this implies that T2 is twice or double T1