I'm sorry bobpursley I don't understand your response, please clarify.

When an object of mass m1 is hung on a vertical spring and set into vertical simple harmonic motion, its frequency is 12 Hz. When another object of mass m2 is hung on the spring along with m1, the frequency of the motion is 4 Hz. Find the ratio m2/m1 of the masses.

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Physics HELP!!!!!!!! - bobpursley, Wednesday, April 4, 2007 at 9:12pm
w= sqrt (k/m)

w^2= k/m

(w1/w2)^2=9 = (m1+m2)/m1

9= 1 + m2/m1

check my thinking.

What is it you do not understand?

Algebra leads you to m2/m1= 8

Post the question in which you do not understand.

hi

To find the ratio of m2/m1, we can use the equation for the frequency of simple harmonic motion:

f = 1 / (2π) * √(k / m),

where f is the frequency, k is the spring constant, and m is the mass.

Given that the frequency when m1 is hanging alone is 12 Hz, we can write the equation as:

12 = 1 / (2π) * √(k / m1).

Similarly, when both m1 and m2 are hanging on the spring, the frequency is 4 Hz:

4 = 1 / (2π) * √(k / (m1 + m2)).

To find the ratio m2/m1, we need to solve these two equations.

We know that the square of a ratio is equal to the ratio of the squares. So, we can square both sides of the second equation to get:

16 = 1 / (2π) * √(k / (m1 + m2))^2.

Simplifying this equation further:

16 = 1 / (2π) * k / (m1 + m2).

Now, let's rewrite the first equation by squaring both sides:

144 = 1 / (2π) * √(k / m1)^2.

Simplifying:

144 = 1 / (2π) * k / m1.

Now, we can compare the equations by dividing the second equation by the first equation:

16 / 144 = (1 / (2π) * k / (m1 + m2)) / (1 / (2π) * k / m1).

Simplifying further:

1 / 9 = m1 / (m1 + m2).

To find the ratio m2/m1, we need to isolate m2 on one side of the equation. Starting with the equation above, we can rearrange it:

1 - 1/9 = (m1 + m2) / m1 - 1/9.

Simplifying:

8/9 = (m1 + m2) / m1.

Now, we can solve for m2/m1 by subtracting 1 from both sides of the equation:

8/9 - 1 = (m1 + m2) / m1 - 1.

Simplifying:

-1/9 = m2 / m1.

Finally, multiply both sides by -1 to get the ratio m2/m1 by itself:

m2/m1 = -(-1/9).

Simplifying:

m2/m1 = 1/9.

Therefore, the ratio of the masses is m2/m1 = 1/9.