Question

The superposition of two SHMs of the same direction results in the oscillation of a point according to the law x = x₀cos (2.1 t) cos 50t. Find the angular frequencies of the constituent oscillations and period with which they beat.

• A. 52.1 s^-1,47.9 s^-1,0.2 s
• B. 50 s^-1,2.1 s^-1,0.22s
• C. 52.1 s^-1,47.9 s^-1, 1.5s
• D. None

Answer 1

Answer: (C)

52.1 s^-1,47.9 s^-1, 1.5s

Answer 2

x₀cos(2.1 t)cos50t

$\frac { x _ { 0 } } { 2 }$ [cos52.1t+cos47.9t].

$\frac { \omega _ { 1 } - \omega _ { 2 } } { 2 \pi }$

or T = $\frac { 2 \pi } { \omega _ { 2 } - \omega _ { 1 } } = \frac { 2 \times \pi } { 4.2 }$ = 1.5 s