Two simple harmonic motions are represented by $y_1=5[\sin 2 \pi t+\sqrt{3} \cos 2 \pi t]$ and $y_2=5 \sin \left[2 \pi t+\frac{\pi}{4}\right]$. The ratio of their amplitudes is

When a mass $m$ is connected individually to the springs $k_1$ and $k_2$, the oscillation frequencies are $v_1$ and $v_2$. If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be

One bar magnet is in simple harmonic motion with time period $T$ in an earth's magnetic field. If its mass is increased by 9 times the time period becomes

In a spring block system as shown in figure. If the spring constant $k=9 \pi^2 \mathrm{Nm}^{-1}$, then the time period of oscillation is