Which of the following is incorrect about simple harmonic oscillations of a particle? 

1.	force and acceleration differ in phase by the angle of ${\mathrm{}}^{}$\(90^\circ.\)
2.	force varies linearly with displacement.
3.	velocity is \(90^\circ\) ahead in phase relative to displacement from the mean position.
4.	K.E. is zero at the extreme position(s).

For a particle executing SHM, the graph between its momentum and displacement will be

1. Straight line

2. Hyperbola

3. Parabola

4. Ellipse

A particle executes SHM of amplitude 10 m and period 4 s along a straight line. The velocity of the particle at a distance of 6 m from the mean position is: 

1.  2$\mathrm{\pi }$ m/s

2.  4$\mathrm{\pi }$ m/s 

3.  6$\mathrm{\pi }$ m/s

4.  5.4$\mathrm{\pi }$ m/s

A uniform rod of mass m and length L pivoted from its one end is executing SHM with time period T. If rod suddenly breaks from the middle while passing through its mean position, then the time period of oscillation of remaining half part will be

1.  2T

2.  $\frac{\mathrm{T}}{2}$

3.  $\sqrt{2}\mathrm{T}$

4.  $\frac{\mathrm{T}}{\sqrt{2}}$

A pendulum oscillates about its mean position \(\mathrm{C}.\) The position where the speed of the bob becomes maximum is: (ignore all dissipative forces)

The position x (in centimeter) of a simple harmonic oscillator varies with time t (in second) as $x = 2\cos \left(0.5\mathrm{\pi t} + \frac{\mathrm{\pi }}{3}\right)$. The magnitude of the maximum acceleration of the particle in $\mathrm{cm}/{\mathrm{s}}^2$ is:

1.  $\mathrm{\pi }$/2

2.  $\mathrm{\pi }$/4

3.  ${\mathrm{\pi }}^2$/2

4.  ${\mathrm{\pi }}^2$/4

A horizontal platform is executing simple harmonic motion in the vertical direction with frequency f. A block of mass m is placed on the platform. What is the maximum amplitude of the SHM, so that the block is not detached from it?

1.  $\frac{\mathrm{mg}}{2{\mathrm{\pi }}^2{\mathrm{f}}^2}$

2.  $\frac{\mathrm{mg}}{4{\mathrm{\pi }}^2{\mathrm{f}}^2}$

2.  $\frac{\mathrm{g}}{2{\mathrm{\pi }}^2{\mathrm{f}}^2}$

4.  $\frac{\mathrm{g}}{4{\mathrm{\pi }}^2{\mathrm{f}}^2}$

A body at the end of a spring executes S.H.M. with a period ${\mathrm{T}}_1$ while the corresponding period for another spring is ${\mathrm{T}}_2$. If the period of oscillation with two springs in series is T, then:

1.  $\mathrm{T} = {\mathrm{T}}_1 + {\mathrm{T}}_2$

2.  ${\mathrm{T}}^2 = {\mathrm{T}}_1^2 + {\mathrm{T}}_2^2$

3.  $\frac{1}{\mathrm{T}} = \frac{1}{{\mathrm{T}}_1} + \frac{1}{{\mathrm{T}}_2}$

4.  $\frac{1}{{\mathrm{T}}^2} = \frac{1}{{\mathrm{T}}_1^2} + \frac{1}{{\mathrm{T}}_2^2}$

A body is executing linear S.H.M. At a position x, its potential energy is ${\mathrm{E}}_1$, and at a position y, its potential energy is ${\mathrm{E}}_2$. The potential energy at the position (x + y) is

1.  ${\mathrm{E}}_1 + {\mathrm{E}}_2$

2.  $\sqrt{{\mathrm{E}}_1^2 + {\mathrm{E}}_2^2}$

3.  ${\mathrm{E}}_1 + {\mathrm{E}}_2 + 2\sqrt{{\mathrm{E}}_1{\mathrm{E}}_2}$

4.  $\sqrt{{\mathrm{E}}_1{\mathrm{E}}_2}$