In the answer below, I have assumed the question refers to simple harmonic motion:

For simple harmonic motion, we have the formulas:

#omega=sqrt(k/m)#

and

#omega=2pif#

where #omega# is the angular velocity of the object, #k# is the spring constant, #m# is the mass of the object, and #f# is frequency

By combining the two equations and solving for #f#, we get:

#2pif=sqrt(k/m)#

#f=1/(2pi)sqrt(k/m)#

Since the only values we care about in this problem are #m# and #f#, we can disregard the constant #1/(2pi)# and let #k# be some arbitrary constant, say #1#, just to make this easier:

#f=sqrt(1/m)#

Now we can substitute #m# for #{m, 1/4m, 4m}#

If #m=m#:

#f=sqrt(1/m)#

this is our value to which we will compare quartering and quadrupling the mass to

If #m=1/4m#

#f=sqrt(1/(1/4m))#

#f=sqrt(4/m)#

#f=2sqrt(1/m)#

which is a frequency #2# times the original frequency.

if #m=4m#

#f=sqrt(1/(4m))#

#f=1/2sqrt(1/m)#

which is a frequency #1/2# times the original frequency.

Therefore, when we take one-fourth of the mass, we have a frequency #2# times the original frequency and when we take four times the mass, we have a frequency #1/2# times the original frequency.