$A$ silver atom in a solid oscillates in simple harmonic motion in a specific direction with a frequency of $10^{12} \ s^{-1}$. What is the force constant of the bonds connecting one atom to the others? (Molar mass of silver $= 108 \ g/mol$ and Avogadro number $= 6.02 \times 10^{23} \ mol^{-1}$)

$A$ body of mass $5\; kg$ hangs from a spring and oscillates with a time period of $2\pi\; s$. If the body is removed,the length of the spring will decrease by:

The variation of potential energy $U$ of a harmonic oscillator with respect to displacement $y$ is as shown in the figure. Find the spring constant $K$.

$A$ mass $m$ is suspended separately by two springs of spring constants $k_1$ and $k_2$. The time periods of oscillations in the two cases are $T_1$ and $T_2$ respectively. If the same mass $m$ is suspended by connecting the two springs in parallel (as shown in the figure),then the time period of the oscillation is $T$. The correct relation is:

In the adjacent figure,if the inclined plane is smooth and the springs are identical,then the period of oscillation of this body is

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