The displacement-time graph of a particle executing SHM is shown in the figure. Its displacement equation will be: (Time period = \(2\) second)

1. \(x= 10\sin\left(\pi t+\frac{\pi}{6}\right)\)
2. \(x= 10\sin\left(\pi t\right)\)
3. \(x= 10\cos\left(\pi t\right)\)
4. \(x= 5\sin\left(\pi t+\frac{\pi}{6}\right)\)

All the surfaces are smooth and the system, given below, is oscillating with an amplitude \({A}.\) What is the extension of spring having spring constant \({k_1},\) when the block is at the extreme position?
              

A spring has a spring constant \(k\). It is cut into two parts \(A\) and \(B\) whose lengths are in the ratio of \(m:1\). The spring constant of the part \(A\) will be:
1. \(\dfrac{k}{m}\)
2. \(\dfrac{k}{m+1}\)
3. \(k\)
4. \(\dfrac{k(m+1)}{m}\)

In a simple harmonic oscillation, the graph of acceleration against displacement for one complete oscillation will be:
1. an ellipse
2. a circle
3. a parabola
4. a straight line

Which of the following relationships between the acceleration \(a\) and the displacement \(x\) of a particle involves simple harmonic motion?
1. \(a =   0 . 7 x\)
2. \(a =   - 200 x^{2} \)
3. \(a =   - 10 x\)
4. \(a =   100   x^{3}\)

A spring having a spring constant of \(1200\) N/m is mounted on a horizontal table as shown in the figure. A mass of \(3\) kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of \(2.0\) cm and released. The frequency of oscillations will be:
    

Acceleration of the particle at \(t = \frac{8}{3}~\text{s}\) from the given displacement \((y)\) versus time \((t)\) graph will be?
                 
1. \(\frac{\sqrt{3}\pi^2}{4}~\text{cm/s}^2\)
2. \(-\frac{\sqrt{3}\pi^2}{4}~\text{cm/s}^2\)
3. \(-\pi^2~\text{cm/s}^2\)
4. zero