**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.

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?