Physics - SHM Question with Solution | TestHub

$x_1=2\sin 10t,x_2=4\sin \left(10t+\frac{\pi }{3}\right)$

Resultant amplitude:$A^2=2^2+4^2+2\times 2\times 4\cos 60^{\circ }=28\Rightarrow A=2\sqrt{7}\text{m}$

(A)$x(0)=2\sin 0+4\sin \frac{\pi }{3}=4\times \frac{\sqrt{3}}{2}=2\sqrt{3}\text{m}$Correct.

(B)$v_{max}=A\omega =2\sqrt{7}\times 10=20\sqrt{7}\text{m/s}$Correct.

(C)$a_{max}=A{\omega }^2=2\sqrt{7}\times 100=200\sqrt{7}{\text{m/s}}^2$Correct.

(D)$E=\frac{1}{2}m{\omega }^2{A}^2=\frac{1}{2}\times 0.02\times 100\times 28=28\text{J}$Correct.

Hence all four options.