Select the wrong statement about simple harmonic motion.

(1) The body is uniformly accelerated.

(2) The velocity of the body changes smoothly at all instants.

(3) The amplitude of oscillation is symmetric about the equilibrium position.

(4) The frequency of oscillation is independent of amplitude.

A particle is executing SHM with time period T starting from the mean position. The time taken by it to complete $\frac{5}{8}$ oscillations is:

(1) $\frac{T}{12}$

(2) $\frac{T}{6}$

(3) $\frac{5T}{12}$

(4) $\frac{7T}{12}$

A particle is executing S.H.M. between x = $\pm$ A. The time taken to go from 0 to $\frac{A}{2}$ is T₁ and to go from $\frac{A}{2}$ to A is T_2, then:

(1) T₁ < T₂

(2) T₁ > T₂

(3) T₁ = T₂

(4) T₁ = 2T₂

For a particle executing simple harmonic motion, the amplitude is A and the time period is T. The maximum speed will be:

(1) 4AT

(2) $\frac{2A}{T}$

(3) $2\pi \sqrt{\frac{A}{T}}$

(4) $\frac{2\pi A}{T}$

A particle is executing S.H.M with an amplitude A and has maximum velocity v_0, its speed at displacament $\frac{3\mathrm{A}}{4}$ will be:

(1) $\frac{\sqrt{7}}{4}{v}_0$

(2) $\frac{v_0}{\sqrt{2}}$

(3) v₀

(4) $\frac{\sqrt{3}}{2}{v}_0$

Two particles executing SHM of the same frequency meet at x = +a/2 while moving in opposite directions. The phase difference between the particles is:

(1) $\frac{\pi }{6}$

(2) $\frac{\mathrm{\pi }}{3}$

(3) $\frac{5\mathrm{\pi }}{6}$

(4) $\frac{2\mathrm{\pi }}{3}$

The displacements of two particles executing SHM on the same line are given as
${\mathrm{y}}_1=asin\left(\frac{\mathrm{\pi }}{2}\mathrm{t}+\mathrm{\varphi }\right)$ and ${\text{y}}_2=\mathrm{bsin}\left(\frac{2\mathrm{\pi }}{3}\mathrm{t}+\mathrm{\varphi }\right)$. The phase difference between them at t=1 sec is:

(1) $\mathrm{\pi }$

(2) $\frac{\pi }{2}$

(3) $\frac{\pi }{4}$

(4) $\frac{\pi }{6}$

For a particle showing motion under the force F= -5 (x - 2)², the motion is:

(1) Translatory

(2) Oscillatory

(3) SHM

(4) All of these

For a particle showing motion under the force F= -5(x - 2), the motion is:

(1) Translatory

(2) Oscillatory

(3) SHM

(4) Both (2) & (3)

Two identical springs have the same force constant 73.5 Nm^-1. The elongation produced in each spring in three cases shown in Figure-1, Figure- 2 and Figure- 3 are: (g = 9.8 ms^-2)

(1) $\frac{1}{6}m,\frac{2}{3}m,\frac{1}{3}m$

(2) $\frac{1}{3}m,\frac{1}{3}m,\frac{1}{3}m$

(3) $\frac{2}{3}m,\frac{1}{3}m,\frac{1}{6}m$

(4) $\frac{1}{3}m,\frac{4}{3}m,\frac{2}{3}m$