An object's motion in the x-y plane is given by $\vec r = 3\cos \left( {2t} \right)\hat x + 3\sin \left( {2t} \right)\hat y$. What is the radius of the object's trajectory?

A particle's motion is described by $\vec{r}(t) = 5\cos(\omega t)\hat{i} + 5\sin(\omega t)\hat{j}$, where r is in meters, t is in seconds, and $\omega = 4\pi$ rad/s. What is the particle's acceleration magnitude?

A particle moves so that its position vector is given by $\mathop {\rm{r}}\limits^ o \, = \,\cos {\rm{\omega }}\,{\rm{t}}\,{\rm{\hat x}}\,{\rm{ + }}\,{\rm{sin}}\,{\rm{\omega }}\,{\rm{t}}\,{\rm{\hat y}}{\rm{.}}$ Where ${\rm{\omega }}$ is a constant. Which of the following is true?

The position of a particle is given by $\vec{R} = 3\sin(5\pi t)\hat{i} + 3\cos(5\pi t)\hat{j}$, where R is in meters and t is in seconds. What is the period of the motion?

A particle's position is given by $\vec r = A\cos \left( {\omega t + \phi } \right)\hat x + A\sin \left( {\omega t + \phi } \right)\hat y$, where $A$, $\omega$, and $\phi$ are constants. What type of motion does the particle exhibit?

If the average velocity of a particle in SHM over a specific time interval is zero, what can you conclude about its displacement over that interval?

Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion

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

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)?

A large horizontal surface moves up and down in SHM with an amplitude of 1 cm. if a mass of 10 kg (which is placed on the surface) is to remain continuously is in contact with it. The maximum frequency of SHM will be

A particle executes $SHM$ with an amplitude of $10\,cm$ and the time period of 1 second. Its average speed during one complete oscillation is