# Problem: A mass is oscillating with amplitude A at the end of a vertical spring of spring constant k.(a) The mass is increased by a factor of four. What is true about the period? Choose the best answer. A. The period is halved.B. The period doubles.C. The period increases by a factor of fourD. The period decreases by a factor of four (b) The mass is increased by a factor of four keeping A and k constant. What is true about the total mechanical energy?

###### FREE Expert Solution

Part (a)

Period:

$\overline{){\mathbf{T}}{\mathbf{=}}{\mathbf{2}}{\mathbf{\pi }}\sqrt{\frac{\mathbf{m}}{\mathbf{k}}}}$

The period is directly proportional to the square root of the mass.

###### Problem Details

A mass is oscillating with amplitude A at the end of a vertical spring of spring constant k.

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

A. The period is halved.
B. The period doubles.
C. The period increases by a factor of four
D. The period decreases by a factor of four

(b) The mass is increased by a factor of four keeping A and k constant. What is true about the total mechanical energy?