Question

A mass m is suspended at one end of a spring and the other end of the spring is firmly fixed on the ceiling. If the mass is slightly depressed and released it will execute oscillation.

1. Write down the expression for the frequency of oscillation of the mass.

2. If the spring is cut into two equal halves and one half of the spring is used to suspend the same mass then obtain an expression for the ratio of periods of oscillation in two cases.

3. If this system is completely immersed in water then what happens to the oscillation?

Answer 1

1. f = \(\frac{1}{2π} \sqrt{k/m}\)

2. f₁ = \(\frac{1}{2 \pi} \sqrt{k / m}\)____(1)

3. When spring is cut in to half, spring constant becomes 2k. Hence frequency,

4. If this system is immersed in water, the amplitude of oscillation decrease quickly. Hence system comes to rest quickly.