In the following questions, match column $-I$ with column $-II$ and choose the correct options
$A-P,\,B-Q,\,C-R,\,D-S$
$A-Q,\, B-P,\, C-R,\, D-S$
$A-Q,\, B-P,\, C-S,\, D-R$
$A-P, \,B-Q,\, C-S,\, D-R$
The motion of a mass on a spring, with spring constant ${K}$ is as shown in figure. The equation of motion is given by $x(t)= A sin \omega t+ Bcos\omega t$ with $\omega=\sqrt{\frac{K}{m}}$ Suppose that at time $t=0$, the position of mass is $x(0)$ and velocity $v(0)$, then its displacement can also be represented as $x(t)=C \cos (\omega t-\phi)$, where $C$ and $\phi$ are
A mass hangs from a spring and oscillates vertically. The top end of the spring is attached to the top of a box, and the box is placed on a scale, as shown in the figure. The reading on the scale is largest when the mass is
Two springs of constant ${k_1}$and ${k_2}$are joined in series. The effective spring constant of the combination is given by
A particle at the end of a spring executes simple harmonic motion with a period ${t_1}$, while the corresponding period for another spring is ${t_2}$. If the period of oscillation with the two springs in series is $T$, then
The effective spring constant of two spring system as shown in figure will be