Question

Two strings stretched by 5 cm and 10 cm respectively Ven masses 0.5 kg and 1kg are suspended at the lower abs when display slightly from the mean position and least they will oscillate with time period in the ratio?

Answer 1

The period of an oscillating spring-mass system is;

• `qquad T = 2 pi sqrt(m/k)`

The springs have the same spring constant, `k`, because doubling the mass doubles the extension:

• `{(0.5"kg" harr 5 "cm"), (1 "kg" harr 5 "cm"):} " and " F ( = mg) = kx`

Therefore, as `k` is fixed, `T propto sqrtm`, and:

`T_1/T_2 = (sqrt0.5)/(sqrt1) = 1/sqrt2`