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.

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

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)