Periodic Motion

Q.

A cylindrical piston of mass M slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be

1. 

2. 

3. 

4. 

Q. A massless beam of length 5m is placed on two wedges A and B .If three forces 3kN , 4kN and 5 kN are applied on the beam as shown in the figure , then find normal reaction at A and B.

Q.

A particle has simple harmonic motion. The equation of its motion is

x = 5 sin $(4t-\frac{\pi }{6})$ , where x is its displacement. If the displacement of the

particle is 3 units, then it velocity is

[MP PMT 1994]

1. 

2. 

3. 16

4. 20

Q. Which of the following examples represent periodic motion? (a) A swimmer completing one (return) trip from one bank of a river to the other and back. (b) A freely suspended bar magnet displaced from its N-S direction and released. (c) A hydrogen molecule rotating about its centre of mass. (d) An arrow released from a bow.

Q. the time period of oscillation of a particle whose position varies with time t as x=(sinwt + sin2Wt+sin4wt ) is In the solution, to calculate the lcm , why we have divided by hcf of denominator?

Q.

Two identical particles A and B, each of mass m, are interconnected by a spring of stiffness k. If particle B experiences a force F and the elongation of the spring is x, the acceleration of particle B relative to particle A is equal to

1. 

2. 

3. 

4. 

Q.

The notes of frequency equal to or an integral multiple of fundamental frequency are called

1. Beats

2. Pitch

3. Harmonics

4. Overtones

Q.

What is periodic motion? explain with an example

Q. A particle is moving in a circle of radius R = 3 mwith an angular speed 2 radian per second inclockwise direction as given in the diagram. Theacceleration (in m/s2) of particle at point P is

Q. A uniform solid sphere of mass m and radiusr is suspended in vertical plane from a pt on its periphery .The time period of its oscillation

Q. consider a ring of mass m 1kg and radius r which is connected to an inextensible string which passes over a frictionless puylley the other of string is connected to upper end of massless spring having spring constant 2k k=25ring can rotatein the horizontal position of ring in equilibrium position then time period ofsmall oscillations of ring is

Q. The displacement of a particle is represented by the equation $y={\sin }^3\omega t$. The motion is

1. non-periodic
2. periodic but not simple harmonic
3. simple harmonic with period $2\pi /\omega$
4. simple harmonic with period $\pi /\omega$

Q.

A cylindrical tube, open at both ends, has a fundamental frequency $f_0$ in air.

The tube is dipped vertically into water such that half of its length is inside

water. The fundamental frequency of the air column now is

[RPET 1999; RPMT 1998, 2000; J & K CET 2000;

KCET 2002; BHU 2002; BCECE 2003]

1. 

2. 

3. 

4. 

Q.

Spring force is a restoring force.

1. False

2. True

3. Can’t predict

4. None of the above

Q. 46.Difference between angular velocity and angular frequency in oscillations?

Q.

An Airplane flying straight towards north describes a periodic motion.

1. True
2. False

Q.

A block of mass m, attached to a spring of spring constant k, oscillates on a smooth horizontal table. The other end of the spring is fixed to a wall. If it has a speed v when the spring is at its natural length, how far will it move on the table before coming to an instantaneous rest?

1. .

2. .

3. .

4. None of these

Q. 59. On a horizontal surface a particle is executing SHM of amplitude 20cm amd time period 4secs . Find minimum time taken by it to move from the extreme position to half of the amplitude .

Q.

Which of the following expressions represent simple harmonic motion

[Roorkee 1999]

1. 

2. 

3. 

4. 

Q. Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point, a distance h directly above the tunnel. The motion of the particle as seen from the earth is
(a) simple harmonic
(b) parabolic
(c) on a straight line
(d) periodic

Q. A particle is moving in a circular path of radius 1 m.if its angular speed is 2pi rad/sec

Q. A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will
(a) remain T
(b) become 2T
(c) become T/2
(d) become $T/\sqrt{2}$

Q.

When a body repeats its motion in regular interval of time then it's said to execute periodic motion. Let's say a car is going on a race track (as shown in figure)

The car covers 5 laps.

For each lap it took 10 mins

In which of the below mentioned cases will its motion be considered periodic.

Case I: The car was travelling with constant speed.

Case II: The car had a constant acceleration from rest (0 m/s) and then a constant deceleration to rest (0 m/s) in each lap for all 5 laps.

Case III: The car had a non-uniform acceleration throughout the journey.

Case IV: lap 1 with constant speed, lap 2 with constant acceleration, lap 3, 4, 5 with variable acceleration.

1. Case I is periodic

2. Case II is periodic

3. Case III is Periodic

4. All cases are periodic

Q. A particle is moving in a circle with uniform speed. Its motion is

1. not periodic
2. periodic and simple harmonic
3. periodic but not simple harmonic
4. none of the above

Q.

Which of the following are necessary conditions for a particle performing periodic motion?

(i) The particle's path is fixed

(ii) The particle's momentum is constant

(iii) Velocity at any position is same after time t = T time duration where T is particle's Time period.

(iv) Time period is same for every cycle

1. All of these

2. (i), (ii), (iv)

3. (i), (iv)

4. (i), (iii), (iv)

Q. Explain why restoring force doesnot depend on the amplitude instead of being displaced?

Q.

how can we define shm?

Q. The frequency of vibration of a string may depend upon length , tension and mass per unit length of the string.Use method of dimension for establishing the formula for frequency

Q. A particle is moving in a circle with uniform speed. Its motion is

1. none of the above
2. periodic and simple harmonic
3. periodic but not simple harmonic
4. not periodic

Q.

Figure 14.27 depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?

(a)

(b)

(c)

(d)