A particle connected to the end of a spring executes S.H.M. with period '$$T_1$$'. While the corresponding period for another spring is '$$\mathrm{T}_2$$'. If the period of oscillation with two springs in series is 'T', then

'$$n$$' waves are produced on a string in 1 second. When the radius of the string is doubled, keeping tension same, the number of waves produced in 1 second for the same harmonic will be

A body of mass '$$m$$' performs linear S.H.M. given by equation $$x=P \sin \omega t+Q \sin \left(\omega t+\frac{\pi}{2}\right)$$. The total energy of the particle at any instant is

A mass $$0.4 \mathrm{~kg}$$ performs S.H.M. with a frequency $$\frac{16}{\pi} \mathrm{Hz}$$. At a certain displacement it has kinetic energy $$2 \mathrm{~J}$$ and potential energy $$1.2 \mathrm{~J}$$. The amplitude of oscillation is