The velocity of a particle executing simple harmonic motion along $x$-axis is described as $v^2=50-x^2$, where $x$ represents displacement. If the time period of motion is $\frac{x}{7} \mathrm{~s}$, the value of $x$ is $\_\_\_\_$ .

A body of mass 2 kg begins to move under the influence of time dependent force $\overrightarrow{\mathrm{F}}=\left(2 \mathrm{t} \hat{\mathrm{i}}+6 \mathrm{t}^2 \hat{\mathrm{j}}\right) \mathrm{N}$, where $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ are unit vectors along $x$ and y -axis respectively. The power produced by the force at $t=2 \mathrm{~s}$ is $\_\_\_\_$ W.

An inductor of 10 mH , capacitor of $0.1 \mu \mathrm{~F}$ and a resistor of $100 \Omega$ are connected in series across an $a . c$ power supply $220 \mathrm{~V}, 70 \mathrm{~Hz}$. The power factor of the given circuit is 0.5 . The difference in the inductive reactance and capacitance reactance is $\sqrt{3} \alpha \Omega$. The value of $\alpha$ is $\_\_\_\_$ .