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) $A\sqrt{2}$

Two identical pendulums oscillate with a constant phase difference $\frac{\mathrm{\pi }}{4}$ and the same amplitude. If the maximum velocity of one is v, the maximum velocity of the other will be:

(1) v

(2) $\sqrt{2}v$

(3) 2v

(4) $\frac{v}{\sqrt{2}}$

A simple pendulum suspended from the ceiling of a stationary lift has period T₀. When the lift descends at a steady speed, the period is T₁, and when it descends with constant downward acceleration, the period is T₂. Which one of the following is true?

(1) T₀ = T₁ = T₂

(2) T₀ = T₁ < T₂

(3) T₀ = T₁ > T₂

(4) T₀ < T₁ < T₂

If a Second's pendulum is moved to a planet where the acceleration due to gravity is 4 times the acceleration due to gravity on earth, to keep the time period of the second's pendulum same, the length of the second's pendulum on the planet should be made:

(1) 2 times

(2) 4 times

(3) 8 times

(4) 15 times

Two pendulums of lengths 1.21 m and 1.0 m start vibrating. At some instant, the two are at the mean position in the same phase. After how many vibrations of the longer pendulum, the two will be in the phase again?

(1) 10

(2) 11

(3) 20

(4) 21

The time period of oscillations of a simple pendulum is 1 minute. If its length is increased by 44%, then its new time period of oscillations will be:

(1) 96 s

(2) 58 s

(3) 82 s

(4) 72 s

A simple pendulum is oscillating in a trolley moving on a horizontal straight road with constant acceleration a. If the direction of motion of the trolley is taken as positive x-direction and the vertically upward direction as positive y-direction, then the mean position of the pendulum makes an angle:

(1) ${\tan }^{-1}\left(\frac{g}{a}\right)$ with y-axis in +x direction

(2) ${\tan }^{-1}\left(\frac{\mathrm{a}}{g}\right)$ with y-axis in -x direction

(3) ${\tan }^{-1}\left(\frac{\mathrm{a}}{g}\right)$ with y-axis in +x direction

(4) ${\tan }^{-1}\left(\frac{g}{a}\right)$ with y-axis in -x direction