The displacement of a particle executing SHM is given by $$x=3 \sin \left[2 \pi t+\frac{\pi}{4}\right]$$, where $$x$$ is in metre and $$t$$ is in seconds. The amplitude and maximum speed of the particles is

A pendulum oscillates simple harmonically and only if

I. the sizer of the bob of pendulum is negligible in comparison with the length of the pendulum.

II. the angular amplitude is less than $$10^{\circ}$$.

Choose the correct option.

A tray of mass $$12 \mathrm{~kg}$$ is supported by two identical springs as shown in figure. When the tray is pressed down slightly and then released, it executes SHM with a time period of $$1.5 \mathrm{~s}$$. The spring constant of each spring is

A piston is performing S.H.M. in the vertical direction with a frequency of $$0.5 \mathrm{~Hz}$$. A block of $$10 \mathrm{~kg}$$ is placed on the piston. The maximum amplitude of the system such that the block remains in contact with the piston is