Oscillations and Waves II

11. Spring Factor K = F/y
12. Period Of oscillation of a mass ‘m’ suspended from a massless spring of force constant ‘k’

For two springs of spring factors k₁ to k₂ connected in parallel effective spring factor

13.For two springs connected in series, effective spring factor ‘k’ is given as

Note:- When length of a spring is made ‘n’ times its spring factor becomes times and hence time period increases √n times.

14. When spring is cut into ‘n’ equal pieces, spring factor of each part becomes ‘nk’.

15. Oscillation of simple pendulum

16. For a liquid of density ρ contained in a U-tube up to height ‘h’

17.For a body dropped in a tunnel along the diameter of earth

18. Resonance: If the frequency of driving force is equal to the natural frequency of the oscillator itself, the amplitude of oscillation is very large then such oscillations are called resonant oscillations and phenomenon is called resonance.

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