The amplitude of a simple harmonic oscillator is \(A\) and speed at the mean position is \(v_0\). The speed of the oscillator at the position \(x={A \over \sqrt{3}}\) will be:

1.	\(2v_0 \over \sqrt{3}\)	2.	\(\sqrt{2}v_0 \over 3\)
3.	\({2 \over 3}v_0\)	4.	\(\sqrt{\frac{2}{3}}v_0\)

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?
              

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.

Acceleration-time (\(a\text-t\)) graph for a particle performing SHM is shown in the figure. Select the incorrect statement.

The graph between the velocity \((v)\) of a particle executing SHM and its displacement \((x)\) is shown in the figure. The time period of oscillation for this SHM will be:

      
1. \(\sqrt{\frac{\alpha}{\beta}}\)
2. \(2\pi\sqrt{\frac{\alpha}{\beta}}\)
3. \(2\pi\left(\frac{\beta}{\alpha}\right)\)
4. \(2\pi\left(\frac{\alpha}{\beta}\right)\)