Question

A $20gm$ particle is subjected to two simple harmonic motions $x_1=2\sin 10t,x_2=4\sin (10t+\frac{\pi }{3})$. Where $x_1$ and $x_2$ are in metre and t is in sec

• A. the displacement of the particle at t=0 will be $2\sqrt{3}$ m
• B. maximum speed of the particle will be $20\sqrt{7}$ m/s
• C. magnitude of maximum acceleration of the particle will be $200\sqrt{7}m/s^2$
• D. energy of the resultant motion will be 28 J

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A energy of the resultant motion will be 28 J
B the displacement of the particle at t=0 will be $2\sqrt{3}$ m
C maximum speed of the particle will be $20\sqrt{7}$ m/s
D magnitude of maximum acceleration of the particle will be $200\sqrt{7}m/s^2$

At $t=0,$

$Displacement,x=x_1+x_2=4sin\left(\frac{\pi }{3}\right)=2\sqrt{3}m$

Resulting amplitude $A=\sqrt{2^2+4^2+2\left(2\right)\left(4\right)\frac{cos\pi }{3}}$

$=2\sqrt{7}m$

maximum speed , $A\omega =20\sqrt{7}\frac{m}{s}$

Energy of the motion $=\frac{1}{2}m{\omega }^2{A}^2=28J$