Question

Design an experiment to find the relationship between the mass on the spring and the period of oscillation. Include: What quantity will you vary?

Which quantities will you hold constant?

What quantities will you measure?

What will you plot?

Answer 1

Apparatus required :

(1) A spring with spring constant, say, k.

(2) Some masses, preferably 5-6 of them under 1 kg each, having a 100 g or 200 g difference between them.

(3) A holder, where the spring can be freely suspended.

(4) A hook to attach the masses to the spring.

When a mass, say 'm', is hung from the spring and the system starts oscillation, time period of the oscillation is : T = 2 ( m / k ).

We now need to measure the time 't' of, say 'n' number of oscillations, and then find the time period using : T = t / n. The number n can be 10, or 20 etc, to reduce the error in measurement.

This same procedure should be repeated for different masses 'm'. Thus, we are varying the mass hung from the spring in each measurement.

The spring should be same in each case, i.e., the spring constant should not be changed during the experiment.

The formula for time period gives :

( T² / m ) = ( 4² / k ).

Hence, if we plot T² ( on y - axis ) as a function of the independent variable m ( on x - axis ), then we should get a straight line, having slope 4² / k.

Hence, from this experiment we can conclude that the time period of an spring - mass system varies directly as the mass hung from the spring.