

$(A)$ the speed of the particle when it returns to its equilibrium position is $u_0$.
$(B)$ the time at which the particle passes through the equilibrium position for the first time is $t=\pi \sqrt{\frac{ m }{ k }}$.
$(C)$ the time at which the maximum compression of the spring occurs is $t =\frac{4 \pi}{3} \sqrt{\frac{ m }{ k }}$.
$(D)$ the time at which the particle passes througout the equilibrium position for the second time is $t=\frac{5 \pi}{3} \sqrt{\frac{ m }{ k }}$.
$y_1 =10 \sin \left(\omega t+\frac{\pi}{3}\right) cm$
$y_2 =5[\sin (\omega t)+\sqrt{3} \cos \omega t] \;cm$ respectively.
The amplitude of the resultant wave is $.............cm$.