A block of mass $$m$$ is connected to a light spring of force constant $$k$$. The system is placed inside a damping medium of damping constant $$b$$. The instantaneous values of displacement, acceleration and energy of the block are $$x, a$$ and $$E$$ respectively. The initial amplitude of oscillation is $$A$$ and $$\omega^{\prime}$$ is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is

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