Question

Find the ratio of time periods oftwo identicalsprings iftheya

Answer 1

We know that if 2 springs are connected in series ( with spring stiffness say k for both) is given by:

1/K (eq)= 1/K + 1/K

Therefore, K(eq) = K/2

And formula for frequency of oscillation of a mass attached to a spring is given by:

f= 1/2 *pie sqrt ( k/m)

So substituting k= k/2 in the above formula gives the frequency of oscillation of mass m in case of series arrangement of springs.

Now, if the 2 springs are connected in parallel then K(eq) =K+K

Therefore, K(eq)=2K

Again substituting 2K in place of K in the frequency formula we get the value of frequency for parallel arrangement of springs.

For ratio, just the divide the frequency obtained in parallel to the frequency obtained in the series arrangement.( As mass of block is taken same for both arrangement).

Answer: 2:1 ( parallel to series)


........... may be this help u.......