A body oscillate with SHM according to equation (SI unit), $x= 10\cos (2πt+π/4)$ at t=1.5 s, calculate the speed of the body.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $44 m s^{-1}$
The equation of a body undergoing SHM is -
$x(t)=10\cos\left(2πt+\frac{π}{4}\right)$
Now,
$v(t)=\frac{dx}{dt}=\left[\frac{d}{dt}\left.\left(10\cos\left(2πt+\frac{π}{4}\right)\right)\right]\right|_{t=1.55}$
$=\left.\left[-20π\sin\left(2πt+\frac{π}{4}\right)\right]\right|_{t=1.55}$
$=-20π×\frac{\sqrt{3}}{2}$
$≃44.2m/s$