The springs in the figure are identical,but the length of the spring in $A$ is three times that in $B$. The ratio of the time periods $T_A/T_B$ is:

$A$ mass attached to a spring is free to oscillate,with angular velocity $\omega$,in a horizontal plane without friction or damping. It is pulled to a distance $x_{0}$ and pushed towards the centre with a velocity $v_{0}$ at time $t=0$. Determine the amplitude of the resulting oscillations in terms of the parameters $\omega, x_{0}$ and $v_{0}$. [Hint: Start with the equation $x=A \cos (\omega t+\theta)$ and note that the initial velocity is negative.]

What is the condition for a body suspended at the end of a spring to undergo simple harmonic oscillation?

Two identical point masses $P$ and $Q$,suspended from two separate massless springs of spring constants $k_1$ and $k_2$,respectively,oscillate vertically. If their maximum speeds are the same,the ratio $(A_Q / A_P)$ of the amplitude $A_Q$ of mass $Q$ to the amplitude $A_P$ of mass $P$ is

The equivalent spring constant of the system as shown in the figure will be:

The frequency of oscillations of a mass $m$ connected horizontally by a spring of spring constant $k$ is $4 \ Hz$. When the spring is replaced by two identical springs connected in series as shown in the figure,the effective frequency is: