Simple Harmonic Oscillation

Q. A rod of mass M and length 2L is suspendedat its middle by a wire. It exhibits torsionaloscillations. If two masses each of m areattached at distance L/2 from its centre onboth sides, it reduces the oscillation frequencyby 20%. The value of ratio m/M is close to

Q. A particle is executing shm about y=0 along y axis. Its position at an instant is given by y= 5 (sin 3pi t+ root3 cos 3pi t) the amplitude of the oscillation is

Q. 19.The displacement from mean position of a particle in SHM at 3 seconds is root3/2 of the amplitude. Its time period will be : (1) 18 sec (2) 6root3 sec (3) 9sec (4) 3root3 sec

Q. For a particle executing simple harmonic motion the displacement from mean position is given by y=asin(wt+ϕ) where a, w, ϕ are constants. Find out velocity of a particle and acceleration of particle.

Q. 35. If distance between earth and sun is increased by 2% then find percentage change in gravitational force acting between them.

Q. two bodies of masses 1kg and 4kg are connected to a vertical spring . the smaller mass executes simple harmonic motion of angular frequncy 25 rad/s and amplitude 1.6mcm while the bigger mass remains stationary on the ground . the maximum force exerted by the system on the floor is?

Q. the amplitude of the simple harmonic motion is Y=(3 sin omega t+4 cos omega t)m

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. The block has a speed $v,$ when the spring is at its natural length. How far will the block move on the table before coming to an instantaneous rest?

1. $x=2v\sqrt{\frac{m}{k}}$
2. $x=\frac{1}{v}\sqrt{\frac{m}{k}}$
3. $x=v\sqrt{\frac{m}{k}}$
4. $x=3\sqrt{\frac{mv}{k}}$

Q. 7. The phase difference between the instantaneousvelocity and acceleration of a particle executingsimple harmonic motion is \lbrack AIPMT (Prelims)-2007\rbrack(1) Zero(3) T(2) 0.5 π(4) 0.707 T

Q.

A particle executes simple harmonic motion along a straight line with an amplitude A. The potential energy is maximum when the displacement is

1. 

2. 

3. ±A

4. Zero

Q. Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? (a) the rotation of earth about its axis. (b) motion of an oscillating mercury column in a U-tube. (c) motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower most point. (d) general vibrations of a polyatomic molecule about its equilibrium position

Q. in earth sun system if sun start to shrink the force on earth due to sun

Q. If somehow the dis†an ce between sun and the Earth is doubled , the gravitational force between them will become a) 2 times b) 1/2 times c)4times d)1/4 time

Q. a particle of mass m is attached to 3 springs a, b, c of equal spring cons†an ts k.the angle between the springs be 120 degrees with particle at its centre.if the particle is pushed against c and released.find the time period of oscillation

Q. the amplitude of simple harmonic motion obtained by combining the motions x1=2sin wt x2= 4sin(wt+pi/6) x3=6sin(wt+pi/3)is

Q. A dipole consists of two particles one with charge $+1\mu C$ and mass $1\text{kg}$ and the other with charge $-1\mu C$ and mass $2\text{kg}$ separated by a distance of 3 m. For small oscillations about its equilibrium position, the angular frequency, when placed in a uniform electric field of $20\text{kV/m}$ is

1. $0.1\text{rad/s}$
2. $1.1\text{rad/s}$
3. $10\text{rad/s}$
4. $2.5\text{rad/s}$

Q.

The distance travelled by a freely falling body is proportional to

1. the mass of the body

2. the square of the acceleration due to gravity

3. the square of the time of fall

4. the time of fall

Q. A block of mass m is attached to one end of a masslessspring which is suspended vertically from a fixedpoint. The mass is held in hand so that the springis neither stretched nor compressed. Suddenly thesupport of the hand is removed. The lowest positionattained by the mass during oscillation is 4 cm belowthe point, where it was held in hand. The amplitudeof the oscillation is(d) 4 cm(c) 3 сm(b) 2 сm(а) 1 cm

Q. A circular spring of natural length $l$ is cut and welded with two beads of masses $m_1$ and $m_2$ such that the ratio of the lengths of the springs between the beads is $4:1$. If the stiffness of the original spring is $k$, then find the angular frequency of oscillation of the beads in a smooth horizontal rigid tube.
[Assume $m_1=m$ and $m_2=3m$].

1. $\omega =\sqrt{\frac{25k}{3m}}$
2. $\omega =\sqrt{\frac{5k}{3m}}$
3. $\omega =\sqrt{\frac{25k}{4m}}$
4. $\omega =\sqrt{\frac{5k}{4m}}$

Q. The mass suspended to the spring is pulled down by 5 cm from equilibrium and released. the mass will oscillate with an amplitude of

Q.

The phase (at a time t) of a particle in simple harmonic motion tells

[AMU (Engg.) 1999]

1. Only the position of the particle at time t

2. Both the position and direction of motion of the particle at time t

3. Only the direction of motion of the particle at time t

4. Neither the position of the particle nor its direction of motion at time t

Q. A thin rod of mass m and length l is suspended from one of its ends. It is set into oscillation about a horizontal axis and its angular speed is Omega while passing through its mean position. How high will its centre of mass rise from its lowest position?

Q. A second pendulum is moved to moon where acceleration due to gravity is 1/ 6times that of earth the leght of second s pendulum on moon will be

Q.

Three smooth pulleys are connected by a light string. A mass m is attached to the pulley $P_3$. Assume the strings between two pulleys and between the pulley and the support to be vertical. If all the pulleys are massless then the tension in the string over the pulleys is

1. 

2. Mg

3. 2mg

4. zero

Q.

The angular frequency of motion whose equation is $4\frac{d^{2}y}{d{t}^2}+9y=0$ is ($y$=displacement and $t$=time)

Q. A force $F=(a+2x-bx)\text{N}$ is acting on a body of mass $4\text{kg},$ which is moving in a straight line. Is the body moving in simple harmonic motion ? If yes, find the equilibrium position of the particle.
[Assume $a>2,b>2$]

1. No
2. $\text{Yes},\frac{a}{(b+2)}$
3. $\text{Yes},\frac{(b-2)}{a}$
4. $\text{Yes},\frac{a}{(b-2)}$

Q. Two blocks of mass $1\text{kg and 2 kg}$ are connected by a vertical spring of spring constant $k=2000\text{N/m}$ such that the $2\text{kg}$ block is resting on the floor (assume frictionless). The upper block of mass $2\text{kg}$ is pushed down by a distance $x$ and released, and it executes $SHM$. What is the maximum value of $x$ so that the $2\text{kg}$ block does not leave the floor?

1. $5\text{mm}$
2. $10\text{mm}$
3. $15\text{mm}$
4. none of the above

Q. what is pseudo force in non inertial frame

Q. Is simple harmonic motion is periodic motion? What are necessary conditions for SHM?

Q. In the arrangements shown in the figure below, block $A$ is connected to a spring and another block $B$ rests on $A$ and the system performs simple harmonic motion with a time period of $2\text{sec}$. The coefficient of static friction between $A$ and $B$ is $0.6$. The maximum amplitude of oscillation which the system can have, so that there is no relative motion between $A$ and $B$ is:
[Take $g=10{\text{m/s}}^2\&{\pi }^2\approx 10$]

1. $0.3\text{m}$
2. $0.6\text{m}$
3. $0.4\text{m}$
4. $0.52\text{m}$