A point mass is subjected to two simultaneous sinusoidal displacements in x -direction, x₁(t)=A t and x₂(t)=A ( t+ 2 3 ) . Adding a third sinusoidal displacement x₃(t)=B ( t+ ) bring the mass to a complete rest. The values of B and are

Step-by-step solution

Resultant amplitude of x₁ and x₂ is A at angle ( 3 ) from A₁ . To make resultant of x₁, x₂ and x₃ to be zero. A₃ should be equal to A at angle = 4 3 as shown in figure. Correct answer is (b). Alternate Solution If we substitute, x₁+x₂+x₃=0 or A t+A ( t+ 2 3 ) +B ( t+ )=0 Then, by applying simple mathematics, we can prove that array rlrl B & =A and & & = 4 3 array Analysis of Question (i) Question is simple. (ii) Question can be solved by applying mathematics also. (iii) Amplitudes of two or more sine or cosine func