Answer:
(a) T = 1.41 T₁ = 3.36 s
(b) T = 0.5 T₁ = 1.19 s
(e) The amplitude does not depend on the variation of m and k.
Explanation:
The period of a block oscillating on a spring is giving by the next equation:
[tex] T = 2\pi \sqrt\frac{m}{k} [/tex] (1)
where m: block's mass, and k: spring constant
(a) If the block's mass is doubled, the period will be:
[tex] T = 2\pi \sqrt\frac{2m}{k} = \sqrt2 \cdot 2\pi \sqrt \frac{m}{k} = 1.41 \cdot T_{1} = 1.41 \cdot 2.38 s = 3.36 s [/tex]
So, the period increase with the increase of the mass.
(c) If the value of the srping constant is quadrupled, from equation (1):
[tex] T = 2\pi \sqrt\frac{m}{4k} = \frac{1}{\sqrt4} 2\pi \sqrt \frac{m}{k} = \frac{1}{2} T_{1} = 0.5 \cdot 2.38 s = 1.19 s [/tex]
The period decrease with the increase of the spring constant.
(e) The oscillation amplitude does not have a relation with m and k, and hence with the period, so if the m and k change or not, the amplitude is the same as the start.
Have a nice day!
