The displacement of an oscillator is given by $x = a\, \sin \, \omega t + b\, \cos \, \omega t$. where $a, b$ and $\omega$ are constant. Then :-

- A
Motion is simple harmonic but not periodic

- B
Motion is periodic but not simple harmonic

- C
Motion is simple harmonic as well as periodic

- D
Motion is neither simple harmonic nor periodic

The displacement of a particle varies according to the relation $x = 3 \sin 100 \, t + 8 \cos ^2 50\,t $. Which of the following is/are correct about this motion .

Two pendulums have time periods $T$ and $5T/4.$ They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum they will be again in the same phase **:**

Define amplitude of $SHM$ and draw two different $SHM$ in one figure having for two different amplitudes.

Vertical displacement of a plank with a body of mass $'m'$ on it is varying according to law $y = \sin \omega t + \cos \omega t.$ The minimum value of $\omega $ for which the mass just breaks off the plank and the moment it occurs first after $t = 0$ are given by **:** ( $y$ is positive vertically upwards)

Two particles are executing S.H.M. The equation of their motion are ${y_1} = 10\sin \left( {\omega \,t + \frac{{\pi T}}{4}} \right),$ ${y_2} = 25\sin \,\left( {\omega \,t + \frac{{\sqrt 3 \pi T}}{4}} \right)$. What is the ratio of their amplitude