Inside a lift, a spring (force constant $k = 1000 \ N/m$) and a block $(mass = 1 \ kg)$ are both in a state of rest. Now, the lift suddenly starts moving upwards with an acceleration $a = g$. Find the maximum total compression in the spring in centimeters. $(g = 10 \ m/s^2)$

Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig. $1$ shows one of them and Fig. $2$ shows their series combination. The ratio of the time period of oscillation of the two $SHM$ is $\frac{T_b}{T_a} = \sqrt{x}$,where the value of $x$ is (Round off to the Nearest Integer).

$A$ mass $m$ is vertically suspended from a spring of negligible mass; the system oscillates with a frequency $n$. What will be the frequency of the system if a mass $4m$ is suspended from the same spring?

Two particles $A$ and $B$ of masses $m$ and $2m$ are suspended from massless springs of force constants $K_1$ and $K_2$. During their oscillation,if their maximum velocities are equal,then the ratio of amplitudes of $A$ and $B$ is

Two identical springs of constant $K$ are connected in series and parallel as shown in the figure. $A$ mass $M$ is suspended from them. The ratio of their frequencies in series to parallel combination will be

$A$ body of mass $M$ and charge $q$ is connected to a spring of spring constant $k$. It is oscillating along the $x-$ direction about its equilibrium position,taken to be at $x = 0$,with an amplitude $A$. An electric field $E$ is applied along the $x-$ direction. Which of the following statements is correct?