Oscillations

A particular of mass m is executing oscillation about the origin on X- axis. Its potential energy is V(x) = K |x|³. Where K is a positive constant. If the amplitude of oscillation is a, then its time period T is proportional to

• $\frac{1}{\sqrt{a}}$

• a

• $\sqrt{a}$

• a^3/2

The displacement of a particle along the x-axis is given by x = a sin² ωt. The motion of the particle corresponds to 

• Simple harmonic motion of frequency ω/π

• Simple harmonic motion of frequency  3ω/2π

• non-simple harmonic motion

• Simple harmonic motion of frequency ω/2π

A girl is swinging on a swinging plate form in sitting position when the girl stands up then the period of swinging?

• Will not change

•  Will depend on height of girl

• Will be longer

•  Will be shorter

The displacement of the motion of a particle is represent by a equation  $\mathrm{Y}=\mathrm{ASin\omega t}+\mathrm{BCos\omega t}$. The motion of the particle is

• SHM with amplitude $\sqrt{{\mathrm{A}}^2+{\mathrm{B}}^2}$

• SHM with amplitude A+B

• SHM with amplitude A

• Oscillatory but not in SHM

Standing wave are produced in a 10 m long stretched string. If the string vibrates in 5 segments and the wave velocity is 20 m/s. The frequency is

• 10Hz

• 5Hz

• 4Hz

• 2Hz

A steel wire 0.5 m long has a total mass 0.01 kg and stretched with a tension of 800 N. The frequency with which it vibrates in its fundamental note will be

• 4Hz

• 2Hz

• 200Hz

• 160Hz

 A cord attached to a vibrating tuning fork is divided into six segments under tension of 36 N. It will be divided into four segments, if the tension is

• 48N

• 81N

• 24N

• 16N

The equation of travelling wave is y= 60 cos (1800 t-6x) where y is in micron and t in second and x in metre. The ratio of maximum particle velocity to velocity of wave propagation is

• 3.6

• 3.6$\times {10}^{-4}$

• $3.6\times {10}^{-11}$

• $3.6\times {10}^{-6}$

In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.170.The frequency of the wave will be

• 2.94Hz

• 0.73Hz

• 0.36Hz

• 1.47Hz

A resonance air column of length 40 cm resonates with tunning fork of frequency 450Hz. Ignoring end corrections , the velocity of sound in air will be

• 1020m/s

• 920m/s

• 820m/s

• 720m/s