Oscillations · Question 22

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m s-2 at a distance of 5 m from the mean position. The time period of oscillation is

1. 2 s
2. s
3. 2 s
4. 1 s

A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is

1. 1 : 9
2. 1 : 11
3. 1 : 14
4. 1 : 6

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in second is

1. 52
2. 4 5
3. 2 3
4. 5

A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is

1. 34
2. 43
3. 169
4. 916

A particle is executing a simple harmonic motion. Its maximum acceleration is and maximum velocity is . Then, its time period of vibration will be

1. 2
2. 2
3. 2 2

A particle is executing SHM along a straight line. Its velocities at distances x1 and x2 from the mean position are V1 and V2 respectively. Its time period is

1. 2 V12+V22x12+x22
2. 2 V12-V22x12-x22
3. 2 x12+x22V12+V22
4. 2 x22-x12V12-V22

When two displacements represented by y1 = a ( t) and y2 = b ( t) are superimposed the motion is

1. simple harmonic with amplitude a2+b2
2. simple harmonic with amplitude (a+b)2
3. not a simple harmonic
4. simple harmonic with amplitude ab

The oscillation of a body on a smooth horizontal surface is represented by the equation, X = A ( t) where X = displacement at time t = frequency of oscillation Which one of the following graphs shows correctly the variation of a with t? Here a = acceleration at time t T = time period

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A particle of mass m oscillates along x-axis according to equation x = a t. The nature of the graph between momentum and displacement of the particle is

1. Circle
2. Hyperbola
3. Ellipse
4. Straight line passing through origin

Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is

1. 6
2. 0
3. 2 3