The displacement of a particle varies according to the relation $x = 3 \sin 100t + 8 \cos^2 50t$. Which of the following is incorrect about this motion?

The function $\sin^2(\omega t)$ represents

$A$ particle moves such that its acceleration $a$ is given by $a = -bx$,where $x$ is the displacement from the equilibrium position and $b$ is a constant. The period of oscillation is

Define displacement variable and periodic function.

$A$ body oscillates with $SHM$ according to the equation (in $SI$ units):
$x = 5 \cos (2 \pi t + \pi / 4)$
At $t = 1.5 \, s$,calculate the:
$(a)$ displacement
$(b)$ speed
$(c)$ acceleration of the body.

Which of the following functions of time represent $(a)$ simple harmonic,$(b)$ periodic but not simple harmonic,and $(c)$ non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant):
$(a)$ $\sin \omega t - \cos \omega t$
$(b)$ $\sin^3 \omega t$
$(c)$ $3 \cos (\pi/4 - 2 \omega t)$
$(d)$ $\cos \omega t + \cos 3 \omega t + \cos 5 \omega t$
$(e)$ $\exp(-\omega^2 t^2)$
$(f)$ $1 + \omega t + \omega^2 t^2$