SHM in Vertical Spring Block

Q. One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance $x_0$ from the block. The spring is then compressed by $2x_0$ and released. The time taken to strike the wall is

1. 
2. 
3. 
4. 

Q.

A mass m attached to a spring oscillates every 2 sec. If the mass is increased by 2 kg, then time-period increases by 1 sec. The initial mass is

1. 9.6 kg
2. 12.6 kg
3. 1.6 kg
4. 3.9 kg

Q.

The left block in figure (12-E13) moves at a speed v towards the right block placed in equilibrium. All collisions to take place are elastic and the surfaces are frictionless. Show that the motions of the two blocks are periodic. Find the time period of these periodic motions. Neglect the widths of the blocks.

Q. As shown in the figure, a block of mass $\sqrt{3}\text{kg}$ is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3\sqrt{3}}$. The critical force to be applied on the vertical surface as shown at an angle ${60}^{\circ }$ with the horizontal such that it does not move will be $3x$. The value of $x$ will be _______. $($up to two decimal places$)$

$[g=10{\text{m/s}}^2;\sin {60}^{\circ }=\frac{\sqrt{3}}{2};\cos {60}^{\circ }=\frac{1}{2}]$

Q. A coin is placed on a horizontal platform, which undergoes vertical simple harmonic motion of angular frequency $\omega$. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time,

1. at the highest position of the platform
2. at the mean position of the platform
3. for an amplitude of $\frac{g}{{\omega }^2}$
4. for an amplitude of $\sqrt{\frac{g}{\omega }}$

Q. A mass m is suspended at the end of a massless wire of length L and cross – sectional area A. If Y is the Young’s modulus of the material of the wire, the frequency of oscillations along the vertical line is given by

1. 
2. 
3. 
4. 

Q. Find the time period of the spring mass system shown in the figure below.

1. $T=2\pi \sqrt{\frac{m}{2K}}$
2. $T=2\pi \sqrt{\frac{m}{K}}$
3. $T=2\pi \sqrt{\frac{2m}{K}}$
4. $T=2\pi \sqrt{\frac{3m}{2K}}$

Q. A spring of force constant k is cut into two parts whose lengths are in the ratio 1:2. The two parts are now connected in the parallel and
a block of mass M is suspended at the end of the combined spring. The time period of oscillation of the block is?

Q. When a body of mass $1.0\text{kg}$ is suspended from a certain light spring hanging vertically, its length increases by $5\text{cm}$. If by replacing the body of mass $1.0\text{kg}$ and suspending $2.0\text{kg}$ block to the spring, the block is pulled through $10\text{cm}$ from its new equilibrium position and released, the maximum velocity achieved by the block is

1. $0.5\text{m/s}$
2. $1\text{m/s}$
3. $4\text{m/s}$
4. $2\text{m/s}$

Q.

What is K In SHM?

Q.

Can a spring constant be negative?

Q. A block of mass $m$ suspended from a spring executes vertical SHM of time period $T$ as shown in the figure. The amplitude of the SHM is $A$ and the spring is never in compressed state during the oscillation. The magnitude of minimum force exerted by the spring on the block is

1. $mg+\frac{4{\pi }^2}{T^2}mA$
2. $mg-\frac{4{\pi }^2}{T^2}mA$
3. $mg-\frac{{\pi }^2}{T^2}mA$
4. $mg+\frac{{\pi }^2}{T^2}mA$

Q. In the system shown in the figure, the string, springs and pulley are weightless. The force constants of the two springs are $k_1=k$ and $k_2=2k$. Block of mass $M$ is pulled vertically down from its equilibrium position and released. Calculate the angular frequency of oscillation.
[Assume the top surface of the block (represented by line $AB$) always remains horizontal]

1. $\omega =\sqrt{\frac{4k}{3M}}$
2. $\omega =\sqrt{\frac{8k}{3M}}$
3. $\omega =\sqrt{\frac{k}{3M}}$
4. $\omega =\sqrt{\frac{2k}{3M}}$

Q.

What happens if the spring constant increases?

Q.

Figure 14.30 (a) shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end. A force F applied at the free end stretches the spring. Figure 14.30 (b) shows the same spring with both ends free and attached to a mass m at either end. Each end of the spring in Fig. 14.30(b) is stretched by the same 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 mass of $10\text{kg}$ is suspended by a rope of length $4\text{m}$, from the ceiling. A force $F$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of ${45}^{\circ }$ with the vertical. Then $F$ equals:
(Take $g=10{\text{ms}}^{-2}$ and the rope to be massless)

1. $100\text{N}$
2. $90\text{N}$
3. $70\text{N}$
4. $75\text{N}$

Q. The coefficient of friction between the blocks of mass $m$ and $2m$ is $\mu =2\tan \theta$. There is no friction between the mass $2m$ and inclined plane. The maximum amplitude of the two block system for which there is no relative motion between both the blocks is:

1. $\frac{mg\sin \theta }{K}$
2. $\frac{3mg\sin \theta }{K}$
3. $g\sin \theta \sqrt{\frac{K}{m}}$
4. $\frac{2mg\sin \theta }{K}$

Q.

Value of spring constant depends upon________.

Q. Two springs of equal lengths and equal cross – sectional areas are made of material whose Young’s modulii are in the ratio of 2 : 3. They are suspended and loaded with the same mass. When stretched and released, they will oscillate with time periods in the ratio of

1. 3: 2
2. 9 : 4
3. 
4. 

Q. If the mass of the pulleys shown in figure is very very small and the cord is inextensible, the angular frequency of oscillation of the system is

1. $\sqrt{\frac{k_a+k_b}{m}}$
2. $\sqrt{\frac{4k_a{k}_b}{(k_a+k_b)m}}$
3. $\sqrt{\frac{k_a{k}_b}{(k_a+k_b)m}}$
4. $\sqrt{\frac{k_a{k}_b}{4m(k_a+k_b)}}$

Q.
A spring block system with mass M and spring constant k is suspended vertically and left to oscillate. It has a natural frequency fo f1. Another spring block system with same mass and spring constant is kept on a horizontal smooth surface.Its natural frequency is observed to be f2.
What do you think will be the relation between f1 and f2.

1. f1=f2
2. Data Insufficient
3. f1>f2
4. f1<f2

Q. The co-efficient of friction between a block of mass $m_2$ and inclined plane is $\mu$. Mass $m_1$ connected to $m_2$ by an inextensible string will starts moving downwards if

1. $\frac{m_1}{m_2}>\sin \theta +\mu \cos \theta$
2. $\frac{m_1}{m_2}<\sin \theta +\mu \cos \theta$
3. $\frac{m_1}{m_2}=\sin \theta +\mu \cos \theta$
4. $\frac{m_1}{m_2}>\sin \theta -\mu \cos \theta$

Q. A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of $40\text{cm}$. The block just loses contact with the plank when the latter is at momentary rest. Then, the period of oscillations is (in seconds):
[Take $g=10{\text{m/s}}^2$]

1. $\frac{2\pi }{5}$
2. $\frac{2\pi }{10}$
3. $\frac{4\pi }{5}$
4. $\frac{3\pi }{10}$

Q.

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released, so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes $\frac{5T}{3}$. Then the ratio of $\frac{m}{M}$ is

1. 25/9

2. 16/9

3. 5/3

4. 3/5

Q. Figure shows the top view of a horizontal surface. Two blocks each of mass $m$ are placed on the surface and connected with a string. The friction coefficient is $\mu$ for each block. A horizontal force $F$ is applied on one of the blocks as shown in the figure. $F$ has the maximum value such that there is no sliding at any contact. Then:

1. If $\theta ={30}^{\circ },F=\frac{2\mu mg}{\sqrt{3}}$ & $T<\mu mg$
2. If $\theta ={45}^{\circ },F=\sqrt{2}\mu mg$ & $T=\mu mg$
3. If $\theta ={60}^{\circ },F=2\mu mg$ & $T<\mu mg$
4. If $\theta ={60}^{\circ },F=\sqrt{3}\mu mg$ & $T=\mu mg$

Q. A body of mass $m$ hangs from a smooth fixed pulley $P_1$ by an inextensible string fitted with the springs of stiffness constants $k_1$ and $k_3$ The string passes over a smooth light pulley $P_2$ , which is connected with another ideal spring of stiffness constant $k_2$. Find the period of small oscillations of the body.

1. $T=2\pi {\left(m(\frac{2}{k_1}+\frac{4}{k_2}+\frac{2}{k_3})\right)}^{\frac{1}{2}}$
2. $T=2\pi {\left(m(\frac{2}{k_1}+\frac{2}{k_2}+\frac{2}{k_3})\right)}^{\frac{1}{2}}$
3. $T=2\pi {\left(m(\frac{1}{k_1}+\frac{1}{k_2}+\frac{1}{k_3})\right)}^{\frac{1}{2}}$
4. $T=2\pi {\left(m(\frac{1}{k_1}+\frac{4}{k_2}+\frac{1}{k_3})\right)}^{\frac{1}{2}}$

Q. A spring block system is kept vertically and the block is in equilibrium position. This equilibrium position is _______

1. Stable
2. Unstable
3. Neutral

Q.

A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction or damping. It is pulled to a distance x₀ and pushed towards the centre with a velocity v₀ at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters ω, x₀ and v₀. [Hint: Start with the equation x = a cos (ωt+θ) and note that the initial velocity is negative.]

Q.

A block of mass m moves with a speed v towards the right block in equilibrium with a spring. If the surface is frictionless and collistions are elastic, the frequency of collisions between the masses will be :

1. 

2. 

3. $\frac{4}{[\frac{2L}{v}+\frac{1}{\pi }\sqrt{\frac{K}{m}}]}$

4. 

Q.

Two uniform strings A and B made of steel are made to vibrate under the same tension. If the first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the length of the strings is

1. $1:2$

2. $1:3$

3. 1:4

4. 1:5