Question

The superposition of two harmonic oscillations of the same direction results in the oscillation of a point according to the law `x=a cos 2.1 t cos 50.0 t`, where `t` is expressed in seconds. Find the angular frequencies of the constituent oscillations and the period with which they beat.

Answer 1

We write`:`
`a cos 2.1 t cos 50.0 t =(a)/(2){cos 52.1 t + cos 47.9 t }`
Thus the angular frequencies of constituent oscillations are
`52.1x^(-1) ` and` 47.9s^(-1)`
To get the beat period note that the variable amplitude `a cos 2.1 t` becomes maximum ( positive or negative ), when
`2.1t=n pi`
Thus the interval between two maxima is
`(pi)/(2.1)=1.5 s` nearly