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?
             

1.	\({k_1 \over k_1+k_2} \text{A}\)	2.	\({k_2A \over k_1+k_2}\)
3.	\(\mathrm{A}\)	4.	\(\text{A} \over 2\)

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

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. $\frac{k(m+1)}{m}$

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

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: 

Which of the following examples represent simple harmonic motion?

Which of the following relationships between the acceleration '\(a\)' and the displacement '\(x\)' of a particle involves simple harmonic motion?

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 $t=\frac{8}{\mathrm{3 }}$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