Two springs, of force constants $k_1$ and $k_2$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$ If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes
Is the following Statement True or False ?
$1.$ If the spring is cut in two equal piece the spring constant of every piece decreases.
$2.$ Displacement of $SHO$ increases, its acceleration decrease.
$3.$ A system can happen to oscillate, have more than one natural frequency.
$4.$ The periodic time of $SHM$ depend on amplitude or energy or phase constant.
Two identical spring of constant $K$ are connected in series and parallel as shown in figure. A mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillations will be
A mass $m = 8\,kg$ is attahced to a spring as shown in figure and held in position so that the spring remains unstretched. The spring constant is $200\,N/m$. The mass $m$ is then released and begins to undergo small oscillations. The maximum velocity of the mass will be ..... $m/s$ $(g = 10\,m/s^2)$
A spring having with a spring constant $1200\; N m ^{-1}$ is mounted on a hortzontal table as shown in Figure A mass of $3 \;kg$ is attached to the free end of the spring. The mass is then pulled sideways to a distance of $2.0 \;cm$ and released. Determine
$(i)$ the frequency of oscillations,
$(ii)$ maximum acceleration of the mass, and
$(iii)$ the maximum speed of the mass.