SHM expression

Q.

A pendulum suspended from the ceiling of a train has a period T, when the train is at rest. When the train is accelerating with a uniform acceleration a, the period of oscillation will

1. Decrease

2. Remain unaffected

3. Become infinite

4. Increase

Q. Two blocks $A\left(5\text{kg}\right)\text{and B}\left(2\text{kg}\right)$ attached to the ends of a spring of spring constant 1120 N/m are placed on a smooth horizontal plane with spring undeformed. Simultaneously velocities of $3\text{m/s and 10 m/s}$ along the line of the spring in the same direction are imparted to $A$ and $B$ then

1. the amplitude of oscillation of $5\text{kg}$ block is $0.18\text{m}$
2. the first maximum compression occurs after start at $\frac{3\pi }{56}\text{s}$
3. the maximum extension of the spring is $0.50\text{m}$
4. time period of oscillation is $\frac{\pi }{14}\text{s}$

Q.

The amplitude and the periodic time of a S.H.M. are 5cm and 6sec respectively. At a distance of 2.5 cm away from the mean position, the phase will be

1. 

2. 

3. 

4. 

Q. The position of a particle moving along x axis given by x=(-2t3+3t2+5)m.The acc of the particle at the ins†an t its velocity becomes zero i

Q. two particles of masses 1 kg and 2kg are placed at a seperation of 50 m . Assuming that the only force acting on the particles are their mutual gravitation , find the initial accelerations of the two particle

Q. Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion? (a) a = 0.7x (b) a = –200x⁵ (c) a = –10x (d) a = 100x³

Q. A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is (a) at the end A, (b) at the end B, (c) at the mid-point of AB going towards A, (d) at 2 cm away from B going towards A, (e) at 3 cm away from A going towards B, and (f) at 4 cm away from B going towards A.

Q. if the initial speed of a particle is u and its accelaration is given as a=At^3 , where A is cons†an t and t is time , then its final speed v will be given as

Q. A CAR MOVES IN EAST DIRECTION FOR 1 HOUR WITH A SPEED OF 60 KM / HR . AND THEN WITH THE SAME SPEED IN SOUTH DIRECTION FOR 30 MIN . FIND ITS DISPLACEMENT FROM THE STARTING POINT ??

Q. A mass m is at a distance a from the centre of a uniform rod of length l and M. The gravitational force on the mass due to the rod is a) 4GMm/(a+l)^2 b) 4GMm/(4a^2-l^2) c) GMm/a^2 d) GMm/2(a+l)^2

Q. A straight rod of length L extends from x=0 to x=L.The linear mass density of the rod varies with x coordinate is λ=a_0+b_0x^2. The gravitational force experienved by a point mass m at x=-a , is

Q.

A S.H.M. has amplitude a and time period T. The maximum velocity will be

[MP PMT 1985; CPMT 1997; UPSEAT 1999]

1. 

2. 

3. 

4. 

Q. Figure 14.26 (a) shows a spring of force constant k clamped rigidly at one end anda mass m attached to its free end. A force F applied at the free end stretches thespring. Figure 14.26 (b) shows the same spring with both ends free and attached toa mass m at either end. Each end of the spring in Fig. 14.26(b) is stretched by thesame force F. (a) What is the maximum extension of the spring in the two cases ? (b) If the mass in Fig. (a) and the two masses in Fig. (b) are released, what is the period of oscillation in each case ?

Q. A particle executing SHM about y=0 along Y axis. its position at an instant is given by y=(7m)sin(pi t). its average velocity for a time interval 0 to 0.5 s is A) 14 m/s B) 7 m/s C) 1/7 m/s D) 28 m/s

Q. The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed ?

Q. A car moves from X to Y with a uniform speed vu and returns to X with a uniform speed vd. The average speed for this round trip is:- (1) vu+vd/2 (2) 2vdvu/vd+vu (3) \sqrt{vuvd} (4) vdvu/vd+v

Q. Draw the graph between kinetic energy and mass of a body when it moves with uniform velocity.

Q. A spring having with a spring constant 1200 N m–1 is mounted on a horizontal table as shown in Fig. 14.24. A mass of 3 kgis attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. Determine (i) the frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.

Q.

In S.H.M. maximum acceleration is at

[RPET 2001; BVP 2003]

1. Acceleration is constant

2. None of these

3. Amplitude

4. Equilibrium

Q. why is omega at same time called angular velocity and also angular frequency?

Q. the equation of an SHM with amplitude A and angular frequency omega in which all the dis†an ces are measured from one extreme position and time is taken to be zero from other extreme position is ?

Q. The motor of an engine is rotating its axis with an angular velocity of $100\text{rev per min}$. It comes to rest in $15\text{s}$ after being switched off, assuming constant angular deceleration. What is the number of revolutions made by it before coming to rest ?

1. $12.5$
2. $32.6$
3. $40$
4. $15.6$

Q. A particle moves on the curve x²=2y.Angle of its velocity vector with x-axis at the point ( 1 , 1/2 )will be??

Q. four particles of masses m, 2m, 3m and 4m are kept in sequence at the corners of a square of side a. The magnitude of gravitational force acting on a particle of mass m placed at the centre of the square will be

Q. Three particles execute SHM along $x-$ direction with same frequency as $x_1=5\sin \omega t$, $x_2=5\sin (\omega t+{53}^{\circ })$, $x_3=-10\cos \omega t$. Find the amplitude of the resultant SHM.

1. $6\text{units}$
2. $8\text{units}$
3. $10\text{units}$
4. $15\text{units}$

Q.

A block of 10 kg is being pulled by a force of 10 N. Find the acceleration of the block?

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Q. speedA vehicle travels half of the total distance with4y36 km/h and next half with 54 km/h. The averagespeed is(1) 12 ms1(2) 12.5 ms-126 AS(3) 25 ms(4) 7.5ms-1

Q. Prove that y= a sinWT + bcosWT represent simple harmonic motion .find amplitude and initial phase of SHM

Q.

When a wave travels in a medium, the particle displacement is given by
$y(x,t)=0.03sin\pi (2t-0.01x)$
where y and x are expressed in metres and t in seconds. At a given instant of time, the phase difference between two particles 25 m apart is

1. $\frac{\pi }{8}$

2. $\frac{\pi }{4}$

3. $\frac{\pi }{2}$

4. $\pi$

Q. A block of mass $100\text{gram}$ attached to a spring of stiffness $25\text{N/m}$ is lying on a frictionless floor as shown in figure. The block is moved to compress the spring by $8\text{cm}$ and released. If collision with the wall is elastic, find the time period of oscillations.

1. $0.451\text{sec}$
2. $0.5\text{sec}$
3. $0.265\text{sec}$
4. $1\text{sec}$