Question #d9e02

1 Answer
May 13, 2017

See below.

Explanation:

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.