Two identical springs have the same force constant $73.5 \,Nm ^{-1}$. The elongation produced in each spring in three cases shown in Figure-$1$, Figure-$2$ and Figure-$3$ are $\left(g=9.8 \,ms ^{-2}\right)$
$\frac{1}{6} \,m, \frac{2}{3} \,m, \frac{1}{3} \,m$
$\frac{1}{3} \,m, \frac{1}{3} \,m, \frac{1}{3} \,m$
$\frac{2}{3} \,m, \frac{1}{3} \,m, \frac{1}{6} \,m$
$\frac{1}{3} \,m, \frac{4}{3} \,m, \frac{2}{3} \,m$
A body of mass $0.01 kg$ executes simple harmonic motion $(S.H.M.)$ about $x = 0$ under the influence of a force shown below : The period of the $S.H.M.$ is .... $s$
A mass $m$ is attached to two springs of same force constant $K$, as shown in following four arrangements. If $T_1, T_2, T_3$ and $T_4$ respectively be the time periods of oscillation in the following arrangements, in which case time period is maximum?
Five identical springs are used in the following three configurations. The time periods of vertical oscillations in configurations (i), (ii) and (iii) are in the ratio
A $1\,kg$ mass is attached to a spring of force constant $600\,N / m$ and rests on a smooth horizontal surface with other end of the spring tied to wall as shown in figure. A second mass of $0.5\,kg$ slides along the surface towards the first at $3\,m / s$. If the masses make a perfectly inelastic collision, then find amplitude and time period of oscillation of combined mass.
For the damped oscillator shown in Figure the mass mof the block is $200\; g , k=90 \;N m ^{-1}$ and the damping constant $b$ is $40 \;g s ^{-1} .$ Calculate
$(a)$ the period of oscillation,
$(b)$ time taken for its amplitude of vibrations to drop to half of Its inittal value, and
$(c)$ the time taken for its mechanical energy to drop to half its initial value.