A spring is having 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 part A will be

1. $\frac{k}{m}$

2. $\frac{k}{m+1}$

3. k

4. $\frac{k(m+1)}{m}$

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

1. $\mathrm{x}=10$ $\sin \left(\mathrm{\pi t}+\frac{\mathrm{\pi }}{6}\right)$

2. $\mathrm{x}=10$ $\sin \left(\mathrm{\pi t}\right)$

3. $\mathrm{x}=10$ $\cos \left(\mathrm{\pi t}\right)$

4. $x=5$ $\sin \left(\mathrm{\pi t}+\frac{\mathrm{\pi }}{6}\right)$

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

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: 

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

A particle executing SHM crosses points A and B with the same velocity. Having taken 3 s in passing from A to
B, it returns to B after another 3 s. The time period of the SHM will be:

1. 15 s

2. 6 s

3. 12 s

4. 9 s

Acceleration of the particle at $t=\frac{8}{\mathrm{3 }}$s from the given displacement (y) versus time (t) graph will be?
                 

1. $\frac{\sqrt{3}{\mathrm{\pi }}^2}{4}$ $cm/s^2$

2. $-\frac{\sqrt{3}{\mathrm{\pi }}^2}{4}$ $cm/s^2$

3. $-{\mathrm{\pi }}^2$ $\mathrm{cm}/{\mathrm{s}}^2$

4. Zero

The time period of the spring-mass system depends upon:

For a particle executing simple harmonic motion, the kinetic energy is given by \(K=K_{0}cos^{2} \omega t.\) The maximum value of potential energy for the given particle: 

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

1.		2.
3.		4.