Question

A signal f(t) is defined as

$f\left(t\right)=20+\sin (\frac{\pi }{7}t+\frac{\pi }{3})+5\sin (\frac{5\pi }{6}t-\frac{\pi }{4})-\cos (\frac{6\pi }{5}t-\frac{\pi }{6})$

The fundamental frequency of f(t) is $\frac{\pi }{a}rad/sec.$. Then the value of a is ________

• A. 210

Answer 1

The correct option is A 210
${\omega }_1=\frac{\pi }{7},{\omega }_2=\frac{5\pi }{6};{\omega }_3=\frac{6\pi }{5}$

${\omega }_0=\frac{H.C.F[\pi ,5\pi ,6\pi ]}{L.C.M[7,6,5]}$

${\omega }_0=\frac{\pi }{210}=\frac{\pi }{a}$

$\therefore a=210$