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:
1. non-periodic.
2. periodic but not simple harmonic.
3. simple harmonic with period \(2\pi / \omega\).
4. simple harmonic with period \(\pi / \omega\).

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