Question

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

Answer 1

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