Oscillations

The circular motion of a particle with constant speed is

• neither periodic nor SHM

• periodic but not SHM

• SHM but not periodic

• periodic and also SHM

A 10 kg metal block is attached to a spring of spring constant 1000 Nm^-1. A block is displaced from equilibrium position by 10 cm and released. The maximum acceleration of the block is

• 10 ms^-2

• 100 ms^-2

• 200 ms^-2

• 0.1 ms^-2

A pipe of 30 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 1.1 kHz source? Given, speed of sound in air = 330 ms^-1.

• Fifth harmonic

• Fourth harmonic

• Third harmonic

• Second harmonic

The ratio of kinetic energy to the potential energy of a particle executing SHM at a distance equal to half its amplitude, the distance being measured from its equilibrium position is

• 2 : 1

• 3 : 1

• 8 : 1

• 4 : 1

A stretched string is vibrating in the second overtone, then the number of nodes and anti-nodes between the ends of the string are respectively

• 3 and 4

• 4 and 3

• 2 and 3

• 3 and 2

If there is no torsion in the suspension thread, then the time period of a magnet executing SHM is

• $\mathrm{T} = 2\mathrm{\pi } \sqrt{\frac{\mathrm{I}}{\mathrm{MB}}}$

• $\mathrm{T} = \frac{1}{2\mathrm{\pi }} \sqrt{\frac{\mathrm{MB}}{\mathrm{I}}}$

• $\mathrm{T} = 2\mathrm{\pi } \sqrt{\frac{\mathrm{MB}}{\mathrm{I}}}$

• $\mathrm{T} = \frac{1}{2\mathrm{\pi }} \sqrt{\frac{\mathrm{I}}{\mathrm{MB}}}$

A particle executing SHM has a maximum speed of 0.5 ms^-1 and maximum acceleration of 1.0 ms^-2. The angular frequency of oscillation is

• 2 rad s^-1

• 0.5 rad s^-1

• $2\mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{-1}$

• $0.5 \mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{-1}$

Two simple pendulums A and B are made to oscillate simultaneously and it is found that A completes 10 oscillations in 20 sec and B completes 8 oscillations in 10 sec. The ratio of the length of A and B is

• $\frac{25}{64}$

• $\frac{64}{25}$

• $\frac{8}{5}$

• $\frac{5}{4}$