Question

The number of independent constituent simple harmonic motions yielding a resultant displacement equation of the periodic motion as $y=8si{n}^2\left(\frac{t}{2}\right)sin\left(10t\right)$ is:

• A. 8
• B. 6
• C. 4
• D. 3

Answer 1

Answer: (D)

3

The resultant displacement equation of periodic motion is given by

$y=8si{n}^2\left(\frac{t}{2}\right).sin\left(10t\right)$

$y=4.2si{n}^2\left(\frac{t}{2}\right).sin\left(10t\right)$

$y=4[1-cost].sin\left(10t\right)$ (as, $2si{n}^2\left(\frac{t}{2}\right)=1-cost$)

$y=4sin\left(10t\right)-4sin\left(10t\right).cost$

$y=4sin\left(10t\right)-2sin\left(11t\right)-sin\left(9t\right)$ (as, $2sinAtsinBt=sin(A+B)t+sin(A-B)t$)

There are three independent constituent simple harmonic motion.

The correct option is D.