A particle is executing SHM along a straight line. Its velocities at distance x₁ and x₂ from the mean position are v₁ and v₂, respectively. Its time period is

The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

• 80 cm

• 100 cm

• 120 cm

• 120 cm

A uniform rope of length L and mass m₁ hangs vertically from a rigid support. A block of mass m₂ is attached to the free end of the rope. A transverse pulse of wavelength  is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is . The ratio  is,

The equation of a simple harmonic wave is given by

where x nd y are in metres and t is in seconds. The ratio of maximum particle celocity of the wave velocity is

• 2π

• 3π/2

• 3π

• 3π

The oscillation of a body on a smooth horizontal surface is represented by the equation, X = A cos (t)
where, X is the displacement at time t

 is the frequency of the oscillation
Which one of the following graphs shows correctly the variation of a with t?

106.

If n₁, n₂ and n₃ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by,

• 

• 

• 

• 

The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are (velocity of sound = 340 m/s)

• 4

• 5

• 7

• 7

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

• kg ms^-1

• kg ms^-2

• kgs^-1

• kgs^-1

A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 ms^-1. It collides with horizontal springs of force constant 200 Nm^-1. The maximum compression produced in the spring will be

• 0.5 m

• 0.6 m

• 0.7 m

• 0.7 m

A wave travelling  in the positive x- direction having displacement along y- direction as 1 m, wavelength 2π m and frequency of 1/π Hz is represented by

• y = sin(x-2t)

• y= sin (2πx-2πt)

• y= sin (10πx-20πt)

• y= sin (10πx-20πt)