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

A particle of mass 10 g is undergoing SHM of amplitude 10 cm and period 0.1 sec. The maximum value of the force on the particle is about:

(1) 5.6 N

(2) 2.75 N

(3) 3.5 N

(4) 4 N

Which of the following graphs best represents the variation of acceleration 'a' of a particle executing SHM with displacement x?

(1) 

(2) 

(3) 

(4) 

Two masses m₁=1 kg and m₂=0.5 kg are executing SHM together suspended by a massless spring of spring constant 12.5 Nm^-1. When masses are in equilibrium, m₁ is removed without disturbing the system. The new amplitude of oscillation will be:

(1) 30 cm

(2) 50 cm

(3) 80 cm

(4) 60 cm

A mass m is attached to two springs of the same force constant K as shown in the following four arrangements. If $T_1, T_2, T_3$ and $T_4$ respectively be the time periods of oscillations in the following arrangements, in which case time period is maximum?

(1) 

(2) 

(3) 

(4) 

A particle of mass 4 kg moves simple harmonically such that its PE (U) varies with position x as shown in the figure. The period of oscillations is:

(1) $\frac{2\pi }{25} \mathrm{s}$

(2) $\frac{\pi \sqrt{2}}{5} \mathrm{s}$

(3) $\frac{4\pi }{5}$

(4) $\frac{2\pi \sqrt{2}}{5}s$ 

The kinetic energy and potential energy of a particle executing S.H.M. are equal when displacement in terms of amplitude 'A' is:

(1) $\frac{A}{2}$

(2) $\frac{A}{\sqrt{2}}$

(3) $\frac{A\sqrt{2}}{3}$

(4) $A\sqrt{2}$