Springs in Parallel and Series

Q. A particle of mass m is attached to three identical springs A, B, C each of force constant k as shown. If the particle is pushed slightly against the spring A and released, find the time period of oscillations

1. 
2. 
3. 
4. 

Q. A spring of force constant k is cut into three equal pieces. If these three pieces are connected in parallel, the force constant of the combination will be

1. $\frac{k}{3}$
2. k
3. 3k
4. 9k

Q. A simple harmonic motion has an amplitude A & time period T. The time required by it to travel from $x=Atox=\frac{A}{2}$ is

1. 
2. 
3. 
4. 

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. How to do the conversion from MKS system to CGS system and from CGS system to MKS system?

Q.

Consider a simple harmonic motion of time period T. Calculate the time taken for the displacement to change value from half the amplitude to the amplitude.

Q. Standing waves are produced by the superposition of two waves, $y_1=0.05\sin (3\pi t-2x)$ and $y_2=0.05\sin (3\pi t+2x)$, where $x$ and $y$ are expressed in metres and $t$ is in seconds. What is the amplitude of a particle at $x=0.5\text{m}$? Given $\cos {57.3}^{\circ }=0.54$.

1. $2.7\text{cm}$
2. $5.4\text{cm}$
3. $8.1\text{cm}$
4. $10.8\text{cm}$

Q. The springs in fig. $A$ and $B$ are identical but the length of spring $A$ is three times the length of each spring in $B$. The ratio of period $T_A/T_B$ is

1. $\sqrt{3}$
2. $1/3$
3. $3$
4. $1/\sqrt{3}$

Q. Three simple harmonic motions of equal amplitudes A and equal time periods in the same direction combine. The phase of the second motion is ${60}^{\circ }$ ahead of the first and the phase of the third motion is ${60}^{\circ }$ ahead of the second. Find the amplitude of the resultant motion.

1. 2A

2. A

3. 3A

4. 

Q. In the given figure, the block is displaced slightly and released. Then, the time period of oscillation is:

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

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.

How are frequency and period related in simple harmonic motion?

Q.

A phonograph turn table rotates at 50 rev/min. Its angular speed in rad/sec is

1. $8.164\mathrm{rad}.{\sec }^{-1}$

2. $5.23\mathrm{rad}.{\sec }^{-1}$

3. $52.3\mathrm{rad}.{\sec }^{-1}$

4. $81.64\mathrm{rad}.{\sec }^{-1}$

Q. Two identical springs of spring constant $k$ each are connecetd in series and parallel as shown in figure. A mass $M$ is suspended from them. The ratio of their frequencies of vertical oscillation will be

1. $1:2$
2. $2:1$
3. $4:1$
4. $1:4$

Q. A spring of force constant k is cut into three equal pieces. If these three pieces are connected in parallel, the force constant of the combination will be

1. k
2. 3k
3. 9k
4. 

Q. An air chamber of volume V has a neck of cross – sectional area a into which a light ball of mass m can move without friction. The diameter of the ball is equal to that of the neck of the chamber. The ball is pressed down a little and released. If the bulk modulus of air in B, the time period of the resulting oscillation of the ball is given by

1. 
2. 
3. 
4. 

Q. Consider two blocks of masses $5kg$ and $10kg$ as shown connected by a massless spring. A force of $100N$ acts on $10kg$ mass as shown. At a certain instant, the acceleration of $5kg$ mass is $12m{s}^{-2}$. Find the acceleration of $10kg$ mass.

1. $1m{s}^{-2}$
2. $6m{s}^{-2}$
3. $8m{s}^{-2}$
4. $4m{s}^{-2}$

Q. A spring of force constant k is cut into two equal halves. The force constant of each half is

1. k
2. 2k
3. 
4. 

Q.

Amplitude of a wave is a measure of its energy.

1. True
2. False

Q. Four massless springs whose force constants are $2k,2k,k$ and $2k$, respectively, are attached to a mass $M$ kept on a frictionless horizontal plane (as shown in figure). If the other ends of the springs are fixed and the mass $M$ is displaced , then the frequency of oscillation of the system is

1. $\frac{1}{2\pi }\sqrt{\frac{k}{4M}}$
2. $\frac{1}{2\pi }\sqrt{\frac{4k}{M}}$
3. $\frac{1}{2\pi }\sqrt{\frac{k}{7M}}$
4. $\frac{1}{2\pi }\sqrt{\frac{7k}{M}}$

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. 

Q. Which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct dimensionally? In the relations given, y is displacement, a is amplitude, t is time and T is time period.

1. $y=asin\frac{2\pi t}{T}$
2. $y=acos\omega t$
3. $y=\frac{a}{T}sin\left(\frac{t}{a}\right)$
4. $y=a\sqrt{2}(sin\frac{2\pi t}{T}+cos\frac{2\pi t}{T})$

Q.

A trolley of mass m is connected to two identical springs, each of force constant k, as shown in figure. The trolley is displaced from its equilibrium position by a distance x and released. The trolley executes simple harmonic motion of period T. After some time it comes to rest due to friction. The total energy dissipated as heat is (assume the damping force to be weak)

1. 
2. 
3. $\frac{2{\pi }^{2}m{x}^2}{T^2}$
4. $\frac{m{x}^2}{T^2}$

Q. A block $M$ shown in the figure oscillates in a simple harmonic motion with amplitude $A$. The amplitude of the point $P$ is

1. $\frac{k_{1}A}{k_2}$
2. $\frac{k_{2}A}{k_1}$
3. $\frac{k_{1}A}{k_1+k_2}$
4. $\frac{k_{2}A}{k_1+k_2}$

Q.

Find the time period of the oscillation of mass m in figures 12-E4 a, b, c. What is the equivalent spring constant of the pair of springs in each case ?

Q. A particle is performing a linear simple harmonic motion. If the acceleration and the corresponding velocity of the particle are a and v respectively, then which of the following graphs is correct?

1. 
2. 
3. 
4. 

Q. The speed $v$ of a particle moving along x-axis is given by, $v^2=8bx-x^2-12b^2,$ where b is a constant. Find amplitude of oscillations. (b = 2 units)

Q. A spring - block pendulum is shown in the figure. The system is hanging in equilibrium. A bullet of mass m/2 moving with a speed u hits the block from down and gets embedded as shown in the figure. Find the amplitude of oscillation now.

1. $\sqrt{\frac{m{u}^2}{8k}+{\left(\frac{mg}{2k}\right)}^2}$
2. $\sqrt{\frac{m{u}^2}{k}+{\left(\frac{mg}{k}\right)}^2}$
3. $\sqrt{\frac{m{u}^2}{6k}+{\left(\frac{mg}{2k}\right)}^2}$
4. $\sqrt{\frac{m{u}^2}{8k}+{\left(\frac{mg}{2k}\right)}^2}$

Q. Two forces $F_1$ and $F_2$ act on a thin uniform elastic rod placed in space. Force $F_1$ acts at right end of the rod and $F_2$ acts exactly at centre of the rod as shown (both forces act parallel to length of the rod).

$\left(i\right)$ $F_1$ causes extension of rod while $F_2$ causes compression of rod.
$\left(ii\right)$ $F_1$ causes extension of rod $F_2$ also causes extension of rod.
$\left(iii\right)$ $F_1$ causes extension of rod while $F_2$ does not change length of rod.

The correct order of $True/False$ for above statements is

1. $TFF$
2. $FTF$
3. $FFT$
4. $FFF$

Q.

A uniform thin rope of length $12m$ and mass $6kg$hangs vertically from a rigid support and a block of mass $2kg$ is attached to its free end. A transverse short wave train of wavelength $6cm$ is produced at the lower end of the rope. What is the wavelength of the wave train (in $cm$) when it reaches the top of the rope?

1. $12$

2. $3$

3. $9$

4. $6$