## Question 5: How can you compare the masses of tow bodies by observing their frequencies of oscillation when supported by a spring?

Solution

Frequency of mass supported by a spring is given by where f is the frequency of oscillation and k is spring constant.

Now consider two bodies of masses m1 and m2 oscillating through springs of same dimensions and having frequencies f1 and f2, respectively. Applying the above equation, we have, and In order to compare the frequencies, divide equation (1) by equation (2).

Comparison of two quantities means to find the ratio between them, i-e, divide one by another. The quotient gives the value of one quantity (in numerator) for the unit quantity of the other (in denominator).  So if we know the frequencies of oscillations of two bodies, we can find the ratio of the oscillating masses.

Frequency of an oscillating body is

 (a) directly proportional to the mass of the body (b) inversely proportional to the mass of the body (c) inversely proportional to the square of the mass of the body (d) inversely proportional to the root of the mass of the body

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