The displacement of a particle is represented by the equation $y= 3 \cos \left(\frac{\pi}{4}-\omega t \right)$. The motion of the particle is:

The displacement of a particle is represented by the equation;  $y =\sin^{3}\omega t.$ The motion is:

The relations between acceleration and displacement of four particles are given below. Which one of the particles is executing simple harmonic motion?

A particle is acted simultaneously by mutually perpendicular simple harmonic motion $x=a \text{cos}𝜔𝑡$ and $y = a\text{sin} 𝜔 𝑡$. The trajectory of motion of the particle will be:

1. an ellipse

2. a parabola

3. a circle

4. a straight line

The displacement of a particle varies with time according to the relation, $y=a~\text{sin} \omega t+b~\text{cos} \omega t.$

Four pendulums $A,B,C,$ and $D$ are suspended from the same elastic support as shown in the figure. $A$ and $C$ are of the same length, while $B$ is smaller than $A$ and $D$ is large than $A.$ If $A$ is given a transverse displacement,
         

The figure shows the circular motion of a particle. The radius of the circle, the period, the sense of revolution, and the initial position are indicated in the figure. The simple harmonic motion of the ${x\text-}$projection of the radius vector of the rotating particle $P$ will be:

1. $x \left( t \right) = B\text{sin} \left(\dfrac{2 πt}{30}\right)$ 

2. $x \left( t \right) = B\text{cos} \left(\dfrac{πt}{15}\right)$ 

3. $x \left( t \right) = B\text{sin} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)$ 

4. $x \left( t \right) = B\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)$ 

The equation of motion of a particle is $x =a \text{cos} ( \alpha   t )^{2}$. The motion is:

1. periodic but not oscillatory

2. periodic and oscillatory

3. oscillatory but not periodic

4. neither periodic nor oscillatory

A particle executing SHM has a maximum speed of $30$ cm/s and a maximum acceleration of $60$ cm/s².  The period of oscillation is:
1. $\pi$ s
2. $\dfrac{\pi }{2}$ s
3. $2\pi$ s
4. $\dfrac{\pi }{4}$ s