When a mass $m$ is attached to a spring, it normally extends by $0.2\, m$. The mass $m$ is given a slight addition extension and released, then its time period will be
$\frac{1}{7}\, sec$
$1\, sec$
$\frac{{2\pi }}{7}\,sec$
$\frac{2}{{3\pi }}\,sec$
If a spring extends by $x$ on loading, then energy stored by the spring is (if $T$ is the tension in the spring and $K$ is the spring constant)
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.
Fill in the blank : Force constant of spring is $0.5\, Nm^{-1}$. The force necessary to increase the length of $10 \,cm$ of spring will be ..........
A mass attached to a spring is free to oscillate, with angular velocity $\omega,$ in a hortzontal plane without friction or damping. It is pulled to a distance $x_{0}$ and pushed towards the centre with a velocity $v_{ o }$ at time $t=0 .$ Determine the amplitude of the resulting oscillations in terms of the parameters $\omega, x_{0}$ and $v_{ o } .$ [Hint: Start with the equation $x=a \cos (\omega t+\theta)$ and note that the initial velocity is negative.]
A spring has spring constant $k$ and $l$. If it cut into piece spring in the proportional to $\alpha : \beta : \gamma $ then obtain the spring constant of every piece in term of spring constant of original spring (Here, $\alpha $, $\beta $ and $\gamma $ are integers)