Springs in Parallel and Series

Q.

The springs shown in the figure are all unstretched in the beginning when a man starts pulling the block. The man exerts a constant force F on the block. Find the amplitude and the frequency of the motion of the block.

1. 

2. 

3. 

4. None of these

Q.

Find the time period of the oscillation of mass m in figures.

(i) $2\pi \sqrt{\frac{m}{k_1+k_2}}$

(ii) $2\pi \sqrt{\frac{m(k_1+k_2)}{k_1{k}_2}}$

(iii) $2\pi \sqrt{\frac{m(k_1-k_2)}{k_1{k}_2}}$

1. (x) - (ii); (y) - (i); (z) - (iii)

2. (x) - (i); (y) - (i); (z) - (ii)

3. (x) - (i); (y) - (ii); (z) - (ii)

4. (x) - (i); (y) - (iii); (z) - (ii)

Q.
Given three setups x, y, z.
Figure out which setup is y similar to.

1. None of them
2. x
3. z
4. Both

Q.

Find the elastic potential energy stored in each spring shown in figure, when the block is in equilibrium. Also find the time period of vertical oscillation of the block.

1. None of these

2. 

3. 

4. 

Q.

A simple harmonic motion of a spring-block system has an amplitude A & time period T. Consider x=0 for equilibrium position. The time required by the block to travel from $x=Atox=\frac{A}{2}$ is -

1. 

2. 

3. 

4. 

Q. Figure shows three identical springs A, B, C. when a 4 kg weight is hung on A, it descends by 1 cm. When a 6kg weight is hung on C, it will descend by

1. 1.5 cm
2. 3.0 cm
3. 4.5 cm
4. 6.0 cm

Q.

A smooth wedge of mass m and angle of inclination 60 degrees rests unattached between two springs of spring constant k and 4k, on a smooth horizontal plane, both springs in the un-extended position. The time period of small oscillations of the wedge (assuming that the springs are constrained to get compressed along their length) equals

1. None of above

2. 

3. 

4. 

Q.

Three S.H.M's of equal amplitude A and equal time period in the same direction combine. The difference in phase between each pair is ${60}^{\circ }$ ahead of the other. The amplitude of the resultant oscillation is :

1. a

2. 2a

3. 4a

4. 0

Q.

A particle of mass m is attached to three springs A, B and C of equal force constants k as shown in figure. if the particle is pushed slightly against the spring C and released, find the time period of oscillation.

1. None of these

2. 

3. 

4. 

Q.

Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is${120}^0$. The resultant amplitude will be

1. A

2. 2A

3. 4A

4.