Physics

Spring Mass Systems

172 Questions

A spring mass system is a key physics concept used to study oscillations and simple harmonic motion. It involves understanding spring constants, damping, and series or parallel combinations. These principles are frequently tested in engineering entrance examinations.

Series and parallel springsSpring constant calculationsDamped oscillationsSpring compression energyElevator systems

Spring Mass Systems Questions

Multiple choice

A vibratory system consists of a mass 12.5 kg, a spring of stiffness 1000 N/m, and a dashpot with damping coefficient of 15 Ns/m.

The value of critical damping of the system is

  1. 0.223 Ns/m

  2. 17.88 Ns/m

  3. 71.4 Ns/m

  4. 223.6 Ns/m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\text{Given m=12.5kg, k=1000Ns/m, c=15Ns/m}\\ \text{Critical Damping,}\\ \hspace{3.2cm}C_c=2m\sqrt{\frac{k}{m}}=2\sqrt{km}\\ \text{On substituting the values, we get}\\ \hspace{3.2cm}C_c=2\sqrt{1000}\times12.5=223.6Ns/m$

Multiple choice

A weighing machine consists of a 2 kg pan resting on a spring. In this condition, the pan resting on the spring, the length of the spring is 200 mm. When a mass of 20 kg is placed on the pan, the length of the spring becomes 100 mm. For the spring, the un-deformed length lo and the spring constant k (stiffness) are

  1. lo = 220mm, k = 1862N / m

  2. lo = 210mm, k = 1960N / m

  3. lo = 200mm, k = 1960 - N / m

  4. lo = 200mm, k = 2156N / m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

In damped oscillatory motion a block of mass 400g is suspended to a spring of force constant 90 N/m in a medium and damping constant is 80g/s. Find time taken for its mechanical energy to drop to half of its initial value 

  1. 4.65 s

  2. 3.465 s

  3. 5 s

  4. 5.46 S
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mechanical energy E(t) = E0 * e^(-2bt), where b = c/(2m). Given m=0.4 kg, c=0.08 kg/s, b = 0.08 / (2 * 0.4) = 0.1 s^-1. We want E(t) = E0/2, so e^(-2 * 0.1 * t) = 0.5. -0.2t = ln(0.5) = -0.693. t = 0.693 / 0.2 = 3.465 s.

Multiple choice resonance oscillations physics

 A mechanical system is oscillating at resonance with a constant amplitude. Which one of the following statements is not correct?

  1. The applied force prevents the amplitude from becoming too large.

  2. The frequency of the applied force is the same as the natural frequency of oscillation of the system.

  3. The total energy of the system is constant.

  4. The amplitude of oscillations depends on the amount of damping.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The applied force prevents the amplitude from becoming too large.


Option A is correct.

Multiple choice physics free, damped and forced oscillations forced vibration forced vibrations free, forced and damped oscillations

A block of $0.5\ kg$ is placed on a horizontal platform. The system is making vertical oscillations about a fixed point with a frequency of $0.5\ Hz.$ Find the maximum amplitude of oscillation if the block is not to lose contact with the horizontal platform?

  1. $0.6542\ m$
  2. $0.9927\ m$
  3. $0.7428\ m$
  4. $0.852\ m$
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice physics rotational motion of a rigid body and moment of inertia motion of rigid body rigid body equilibrium of a rigid body

Three weight $W, 2W$ and $3W$, are connected to identical springs suspended from rigid horizontal rod. The assembly of the rod and the weights fall freely. The positions of the weights from the rod are such that

  1. $3W$ will be farthest
  2. $W$ will be farthest

  3. all will be at the same distance
  4. $2W$ will be farthest
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since all the weights fall freely under gravity along with the assembly of the rod, the acceleration of all objects is equal to $g$. Hence all the weights have same relative distance between them at all points, and hence no stretching of spring occurs and thus the position(distance of falling) of all the weights would be the same.

Multiple choice the nature of electromagnetic waves space exploration and forms of light observing space: telescopes electromagnetic waves physics

A long spring is fixed at one end. A person holding the other end compresses the spring with a jerk. The compression travels along the length of the spring. Which kind of wave is travelled along the length of the spring?

  1. Electromagnetic waves

  2. Transverse waves

  3. Longitudinal waves

  4. Both (A) and (C)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the spring is compressed, particles of the spring come close and there is compression.When spring is extended, particles rarefact from each other . Direction of particle motion is in the direction of wave propagation, Hence longitudinal waves  .


Multiple choice free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

A linear harmonic oscillator of force constant $2 \times$10$^{6}$Nm$^{-1}$ and amplitude 0.01 m has a total mechanical energy of 160 J. Its

  1. maximum potential energy is 100 J

  2. maximum kinetic energy is 100 J

  3. maximum potential energy is 160 J

  4. minimum potential energy is zero.
Reveal answer Fill a bubble to check yourself
B,C Correct answer
Explanation

As, we know total mechanical energy $=$ maximum potential energy

$\therefore \quad ATQ.T.E=160J\Rightarrow Max.P.E.=160J$
$\Rightarrow$  Statement (C) is correct.
Also, for maximum kinetic energy, we know,
$K.E.=\dfrac { 1 }{ 2 } K\left( { x } _{ m }^{ 2 } \right) $
where ${ x } _{ m }=\left( 0.01 \right) m\quad & \quad K=2\times { 10 }^{ 6 }{ Nm }^{ -1 }$
$\Rightarrow K.E.=\left( \dfrac { 1 }{ 2 }  \right) \left( 2\times { 1 }0^{ 6 } \right) { \left( 0.01 \right)  }^{ 2 }=100J$
$\Rightarrow$  Statement (B) is the correct answer.