Question

Two springs of equal lengths and equal cross sectional area are made of materials whose Young's moduli are in the ratio of 2 : 3. They are suspended and loaded with the same mass. When stretched and released they oscillate. Find the ratio of the time period of oscillation.

Answer 1

T=2π✓m/k

Now k=YA/L

let k1 be spring constant of first spring and k2 of second

then k1/k2=Y1/Y2=2/3

T1/T2 =✓k2/✓k1 =✓3/✓2