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. \(\dfrac{k(m+1)}{m}\)

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?
              

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

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

A simple pendulum is pushed slightly from its equilibrium towards the left and then set free to execute the simple harmonic motion. Select the correct graph between its velocity (\(v\)) and displacement (\(x \)).

1.		2.
3.		4.