The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended , the period of oscillation will now be
$T$
$\frac{T}{{\sqrt 2 }}$
$2T$
$\sqrt 2 $$T$
In the figure, ${S_1}$ and ${S_2}$ are identical springs. The oscillation frequency of the mass $m$ is $f$. If one spring is removed, the frequency will become
One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance ${x_0}$ from the black. The spring is then compressed by $2{x_0}$ and released. The time taken to strike the wall is
Infinite springs with force constant $k$, $2k$, $4k$ and $8k$.... respectively are connected in series. The effective force constant of the spring will be
A mass $m$ is suspended by means of two coiled spring which have the same length in unstretched condition as in figure. Their force constant are $k_1$ and $k_2$ respectively. When set into vertical vibrations, the period will be
A mass of $5\, {kg}$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length $4\, {m}$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed? (In ${m} / {s}^{2}$)