SHM Formulae

Q.

A particle is moving on x-axis has potential energy $U=2-20x+5x^2$ J along x-axis. The particle is released at x=-3. The maximum value of x will be [x is in meter and U is in joule]

1. 5 m

2. 7 m

3. 8 m

4. 3 m

Q.

A particle executes simple harmonic motion with an amplitude of 4 cm. At the

mean position the velocity of the particle is 10 cm/s. The distance of the

particle from the mean position when its speed becomes 5 cm/s is

[EAMCET (Med.) 2000]

1. 

2. 

3. 

4. 

Q.

If a particle under S.H.M. has time period 0.1 sec and amplitude 2x${10}^{-3}$ m. It has maximum velocity

[RPET 2000]

1. 

2. 

3. 

4. None of these

Q.

The total energy of a particle executing S.H.M. is proportional to

[CPMT 1974, 78; EAMCET 1994; RPET 1999;

MP PMT 2001; Pb. PMT 2002; MH CET 2002]

1. Displacement from equilibrium position

2. Frequency of oscillation

3. Velocity in equilibrium position

4. Square of amplitude of motion

Q.

Two blocks A and B each of mass m are connected by a massless spring of natural length L and spring constant K. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length as shown in figure. A third identical block C also of mass m moves on the floor with a speed v along the line joining A and B and collides elastically with A. Then

1. The kinetic energy of the A-B system at maximum compression of the spring is zero

2. The kinetic energy of the A-B system at maximum compression of the spring is

3. The maximum compression of the spring is

4. The maximum compression of the spring is

Q.

Two blocks A and B each of mass m are connected by a massless spring of natural length L and spring constant K. The blocks are initially resting on a smooth horizontal floor with spring at its natural length as shown in the figure. A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B and collides with A. Then,

1. The KE of the A-B system at maximum compression of the spring is zero

2. The KE of the AB system at maximum compression of the spring is

3. The maximum compression of the spring is

4. The maximum compression of the spring is

Q. A particle executes $\text{SHM}$ on a line $8\text{cm}$ long. Its $\text{K.E.}$ and $\text{P.E.}$ will be equal when its distance from the mean position is :

1. $4\text{cm}$
2. $2\text{cm}$
3. $2\sqrt{2}\text{cm}$
4. $\sqrt{2}\text{cm}$

Q.

The total energy of the body executing S.H.M. is E. Then the kinetic energy when the displacement is half of the amplitude, is

[RPMT 1994, 96; CBSE PMT 1995; JIPMER 2002]

1. 

2. 

3. 

4. 

Q. A body is executing simple harmonic motion. At a displacement x, its potential energy is $E_1$ and at a displacement $y$, its potential energy is $E_2$. The potential energy $E$ at a displacement $(x+y)$ is

1. $E_1+E_2$
2. $\sqrt{E_1^2+E_2^2}$
3. $E_1+E_2+2\sqrt{E_1{E}_2}$
4. $\sqrt{E_1{E}_2}$

Q.

A particle is moving on x-axis has potential energy $U=2-20x+5x^2$ J along x-axis. The particle is released at x=-3. The maximum value of x will be [x is in meter and U is in joule]

1. 5 m

2. 3 m

3. 7 m

4. 8 m

Q.

Two blocks A and B each of mass m are connected by a massless spring of natural length L and spring constant K. The blocks are initially resting on a smooth horizontal floor with spring at its natural length as shown in the figure. A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B and collides with A. Then,

1. The KE of the A-B system at maximum compression of the spring is zero

2. The KE of the AB system at maximum compression of the spring is $\frac{m{v}^2}{2}$

3. The maximum compression of the spring is $v\sqrt{\frac{m}{k}}$

4. The maximum compression of the spring is $v\sqrt{\frac{m}{2k}}$

Q. A particle executes simple harmonic motion with a frequency f. The frequency with which the kinetic energy oscillates is
[IIT JEE 1987]

1. $\frac{f}{2}$

2. f

3. 2f

4. 4f