The total spring constant of the system as shown in the figure will be
$\frac{{{k_1}}}{2} + {k_2}$
${\left[ {\frac{1}{{2{k_1}}} + \frac{1}{{{k_2}}}} \right]^{ - 1}}$
$\frac{1}{{2{k_1}}} + \frac{1}{{{k_2}}}$
${\left[ {\frac{2}{{{k_1}}} + \frac{1}{{{k_2}}}} \right]^{ - 1}}$
The scale of a spring balance reading from $0$ to $10 \,kg$ is $0.25\, m$ long. A body suspended from the balance oscillates vertically with a period of $\pi /10$ second. The mass suspended is ..... $kg$ (neglect the mass of the spring)
A block whose mass is $1 \;kg$ is fastened to a spring. The spring has a spring constant of $50\; N m ^{-1}$. The block is pulled to a distance $x=10\; cm$ from its equilibrlum position at $x=0$ on a frictionless surface from rest at $t=0 .$ Calculate the kinetic, potentlal and total energles of the block when it is $5 \;cm$ away from the mean position.
Find the ratio of time periods of two identical springs if they are first joined in series $\&$ then in parallel $\&$ a mass $m$ is suspended from them :
Two springs with negligible masses and force constant of $K_1 = 200\, Nm^{-1}$ and $K_2 = 160\, Nm^{-1}$ are attached to the block of mass $m = 10\, kg$ as shown in the figure. Initially the block is at rest, at the equilibrium position in which both springs are neither stretched nor compressed. At time $t = 0,$ a sharp impulse of $50\, Ns$ is given to the block with a hammer.
A mass m oscillates with simple harmonic motion with frequency $f = \frac{\omega }{{2\pi }}$ and amplitude A on a spring with constant $K$ , therefore