The frequency of oscillation of the springs shown in the figure will be
$\frac{1}{{2\pi }}\sqrt {\frac{K}{m}} $
$\frac{1}{{2\pi }}\sqrt {\frac{{({K_1} + {K_2})m}}{{{K_1}{K_2}}}} $
$2\pi \sqrt {\frac{K}{m}} $
$\frac{1}{{2\pi }}\sqrt {\frac{{{K_1}{K_2}}}{{m({K_1} + {K_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.
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
If a spring of stiffness $k$ is cut into two parts $A$ and $B$ of length $l_{A}: l_{B}=2: 3$, then the stiffness of spring $A$ is given by
Two bodies $M$ and $N $ of equal masses are suspended from two separate massless springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude $M$ to that of $N$ is
Springs of spring constants $K, 2K, 4K, 8K,$ ..... are connected in series. A mass $40\, gm$ is attached to the lower end of last spring and the system is allowed to vibrate. What is the time period of oscillation ..... $\sec$. (Given $K = 2\, N/cm$)