Ablock oscillating on a spring has period t1 = 2.38s . note that you do not know the value of either m or k, so do not assume any particular values for them. the required analysis involves thinking about ratios.
part a: what is the period if the block's mass is doubled?
part c: the value of the spring constant is quadrupled?
part e: the oscillation amplitude is doubled while m and k are unchanged?

(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:

(1)

where m: block's mass, and k: spring constant

(a) If the block's mass is doubled, the period will be:

So, the period increase with the increase of the mass.              

(c) If the value of the srping constant is quadrupled, from equation (1):

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!