A particle moves in the x-y plane according to the equation
       $x = A \cos^2 \omega t$ and $y = A \sin^2 \omega t$
Then, the particle undergoes:

A particle of mass $m$ executes SHM along a straight line with an amplitude $A$ and frequency $f.$

The equation of motion of a particle that starts moving at $t=0$ s is given by ${x}=5 \sin \left(\dfrac{\pi t}{2}+\dfrac{\pi}{3}\right)$ where $x$ is in cm and time $t$ is in second. The time, when the particle first comes to rest, is:

The energy of the block is $E$, and the plane is smooth, the wall at the end $B$ is smooth. Collisions with walls are elastic. The distance $AB=l$, the spring is ideal and the spring constant is $k$. The time period of the motion is:
    

A simple pendulum of time period $T_0$ is taken in a rocket which is accelerating upwards initially and then, after some time, it moves with uniform velocity upward. The time period of the pendulum is observed within the rocket and is found to be $2T_0$. The rocket, at that time, must be at a distance (above the earth's surface) of (radius of earth = $R$)

Trains travel between station $A$ and station $B$: on the way up (from $A~\text{to}~B$) - they travel at a speed of $80$ km/h, while on the return trip the trains travel at twice that speed. The services are maintained round the clock. Trains leave station $A$ every $30$ min for station $B$ and reach $B$ in $2$ hrs. All trains operate continuously, without any rest at $A$ or $B$.