The oscillation frequency f cycles per second, of a spring is inversely proportional to the square root of the mass m kg of the spring. When m=2.56, f=2, how do you find f when m=4?

Question

Eli Assouline · Accepted Answer

undefined To find f when m=4, we can use the inverse proportionality relationship between the oscillation frequency and the square root of the mass.

First, we can set up the proportionality equation as follows:

f ∝ 1/√m

Next, we can substitute the given values into the equation:

2 ∝ 1/√2.56

To find the constant of proportionality, we can solve for it:

2 = k/√2.56

Simplifying the equation:

2 = k/1.6

Multiplying both sides by 1.6:

k = 2 × 1.6

k = 3.2

Now that we have the constant of proportionality, we can use it to find f when m=4:

f = k/√m

Substituting the values:

f = 3.2/√4

Simplifying:

f = 3.2/2

f = 1.6

Therefore, when m=4, the oscillation frequency f is equal to 1.6.

Eva Adamson · Answer

#f =+-sqrt(2.56)#

#color(blue)("Determining the appropriate values")# Inversely proportional #->a=k/b# where #k# is the constant of variation. So we have:

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

Initial condition:

#f=1/(sqrt(m))xxk color(white)("dddd") ->color(white)("dddd")2=1/sqrt(2.56)xxk#

So we have: #color(white)("d")->k=2sqrt(2.56)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Answering the question for "m=4)#

#f=1/(sqrt(m))xxk color(white)("ddd")-> color(white)("ddd") f=1/sqrt(4)xx2sqrt(2.56)#

# color(white)("dddddddddddddd")-> color(white)("ddd")f=1/(+-2)xx2sqrt(2.56)#

# color(white)("dddddddddddddd")-> color(white)("ddd")f =+-sqrt(2.56)#