A ball is thrown vertically upwards. Which of the following graphs correctly represents the variation of acceleration with time during its upward motion (neglecting air resistance)?

The minimum phase difference between two simple harmonic oscillations, ${y_1} = \frac{1}{2}\sin \,\,\omega t + \frac{{\sqrt 3 }}{2}\cos \,\,\omega t$ ${y_2} = \sin \,\,\omega t + \cos \,\,\omega t,$ is

A particle executing S.H.M. of amplitude 4 $cm$ and $T$=4 s. The time taken by it to move from positive extreme position to half the amplitude is

The displacement of a particle varies according to the relation x=4(cos⁡πt+sin⁡πt). The amplitude of the particle is

The displacement of a particle executing SHM is given by $y = 0.25{\rm{ }}sin{\rm{ }}200t{\rm{ }}\,\,\,cm$ the maximum speed of the particle is

The displacement of two identical particle executing SHM are represented by equations {x_1}$$ = \,\,8\,\,\sin $(10\,\,t + \;\;\pi /6\,\,)$ and ${x_2} = 5\,\,\sin \,\,\omega t.$ For what value of ω energy of both the particle is same?

The motion which is not simple harmonic is

A particle executes $SHM$ with amplitude $0.5\,cm$ and frequency $100\,\,{s^{ - 1}}$. The maximum speed of the particle is $\left[ {in\,\,m/s} \right]$

The velocities of a body executing $SHM$ are $3\,cm/s$ and $4\,cm/s$. When the displacements are $4\,cm$ and $3\,cm$ respectively then period is

The ratio of the magnitudes of maximum velocity to the maximum acceleration of a particle making $SHM$ is $1:1$. The minimum time taken by the particle to move between the extreme points of its path is

The position vector of a particle $\vec{R}$ as a function of time is given by: $\vec{R} = 6\sin(2\pi t)\hat{i} + 6\cos(2\pi t)\hat{j}$. Where R is in meters, t is in seconds and $\hat{i}$ and $\hat{j}$ denote unit vectors along x- and y-directions, respectively. Which one of the following statements is wrong for the motion of the particle?