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 physics measurements and units measuring mass measurement of mass measuring instruments

A body is attached to a spring balance suspended from a stand. The reading on the balance is $0.5$kg. The two together are detached from the stand and allowed to fall through a height. While falling the reading in the balance will be.

  1. More than $0.5$ kg depending on the height
  2. Less than $0.5$ kg but not zero

  3. Zero
  4. $0.5$ kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When the spring balance and the body fall together, they are in a state of free fall. In this state, both the body and the spring balance experience the same acceleration due to gravity, meaning there is no net force exerted by the body on the spring. Consequently, the reading on the balance becomes zero.

Multiple choice physics magnetic effect of electric current magnetic field lines due to current magnetic field due to current carrying conductor magnetic field on the axis of a toroid

If a current is passed in a spring it

  1. gets compressed

  2. gets expanded

  3. oscillates

  4. remains unchanged
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Spring can be assumed as the coil parallel to each other.
So, when current flows in spring each coil gets current flow in same direction. So, they are attracted to each other which in turn results in compression of spring.

Multiple choice collisions in one dimension collisions work, energy and power mechanics physics

A spring of natural length 3m and spring constant 9 N/m is having one end at origin and other end attached to a block of mass 1 kg. There is a wall at x=3m. At t=0 block is released from rest at x= 1 m. Collision of block with wall is elastic. Which of the following gives position of block with time :-

  1. $x=cos\left( 3t \right) $
  2. $x=3-2sin\left( 3t+\frac { \pi }{ 2 } \right) $
  3. $x=3-\left| 2cos\left( 3t \right) \right| $
  4. $x=3-2sin\left( 3t+\frac { 3\pi }{ 2 } \right) $
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice collisions in one dimension collisions work, energy and power mechanics physics

A block of mass 100$\mathrm { g }$ attached to a spring of stiffness 100$\mathrm { N } / \mathrm { m }$ is lying on a frictionless floor as shown. block is moved to compress the spring by 10 cm and released. If the collision with the wall is elastic then the time period of oscillations. (in seconds) 

  1. 0.133

  2. 13.3

  3. 0.26

  4. 0.3
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

The energy stored in a spring is:

  1. Kinetic energy

  2. Potential energy

  3. Both kinetic and potential energy
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When a spring is stretched or compressed, it stores potential energy. This energy is due to the elastic properties of the spring, which tend to restore it to its original shape when the force is removed.

Multiple choice

A spring is a device that stores energy when it is stretched or compressed. The potential energy stored in a spring is given by the equation:

  1. U = 1/2kx^2

  2. U = Fd

  3. U = kx
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The potential energy stored in a spring is given by the equation U = 1/2kx^2, where U is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

Multiple choice

A mass-spring system is a system consisting of a mass attached to a spring. The natural frequency of a mass-spring system is the frequency at which the system will oscillate when it is disturbed from its equilibrium position. The equation for the natural frequency of a mass-spring system is:

  1. f = 1/2π√(k/m)

  2. f = Fd

  3. f = kx
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The natural frequency of a mass-spring system is the frequency at which the system will oscillate when it is disturbed from its equilibrium position. The equation for the natural frequency of a mass-spring system is f = 1/2π√(k/m), where f is the natural frequency, k is the spring constant, and m is the mass of the object.

Multiple choice

Which differential equation is used to model the motion of a spring-mass system?

  1. Hooke's Law

  2. Newton's Second Law

  3. Simple Harmonic Motion Equation

  4. Damped Harmonic Motion Equation
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The Simple Harmonic Motion Equation describes the oscillatory motion of a spring-mass system.

Multiple choice

A mass of 10 kg is attached to a spring with a spring constant of 100 N/m. The mass is pulled 5 cm to the right of its equilibrium position and released. What is the equation of motion for the mass?

  1. \(mx'' + kx = 0\)
  2. \(mx'' - kx = 0\)
  3. \(mx'' + kx = 10\)
  4. \(mx'' - kx = 10\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation of motion for a mass-spring system is given by (mx'' + kx = 0), where (m) is the mass, (k) is the spring constant, and (x) is the displacement from the equilibrium position. In this case, (m = 10) kg, (k = 100) N/m, and the initial displacement is (x_0 = 0.05) m. So, the equation of motion is (10x'' + 100x = 0).

Multiple choice

What is the name of the energy stored in a stretched or compressed spring?

  1. Kinetic energy

  2. Potential energy

  3. Internal energy

  4. Thermal energy
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Potential energy is the energy stored in a stretched or compressed spring, and is released when the spring is allowed to return to its original shape.

Multiple choice

In a mechanical system, the equation (m\frac{d^2x}{dt^2} + kx = 0) describes the motion of a mass (m) attached to a spring with spring constant (k). What is the natural frequency of the system?

  1. \(\sqrt{\frac{k}{m}}\)
  2. \(\frac{1}{2\pi}\sqrt{\frac{k}{m}}\)
  3. \(\frac{1}{2\pi}\sqrt{\frac{m}{k}}\)
  4. \(\sqrt{\frac{m}{k}}\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The natural frequency of the system is given by (\omega_n = \sqrt{\frac{k}{m}}).

Multiple choice

A spring-mass system is described by the differential equation (m\frac{d^2x}{dt^2} + kx = F_0\sin(\omega t)), where (m) is the mass, (k) is the spring constant, (F_0) is the amplitude of the applied force, and (\omega) is the angular frequency. What is the steady-state solution for the displacement (x)?

  1. \(x(t) = \frac{F_0}{k}\sin(\omega t)\)
  2. \(x(t) = \frac{F_0}{k}\cos(\omega t)\)
  3. \(x(t) = \frac{F_0}{m\omega^2}\sin(\omega t)\)
  4. \(x(t) = \frac{F_0}{m\omega^2}\cos(\omega t)\)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The steady-state solution for the displacement is given by (x(t) = \frac{F_0}{m\omega^2}\sin(\omega t)).

Multiple choice

In a mass-spring-damper system, the equation (m\frac{d^2x}{dt^2} + c\frac{dx}{dt} + kx = F(t)) describes the displacement (x) of the mass. What is the damping ratio of the system?

  1. \(\frac{c}{2\sqrt{mk}}\)
  2. \(\frac{c}{\sqrt{mk}}\)
  3. \(\frac{2c}{\sqrt{mk}}\)
  4. \(\frac{2c}{m}\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The damping ratio of the system is given by (\zeta = \frac{c}{2\sqrt{mk}}).

Multiple choice

A spring is stretched by 10 cm from its equilibrium position. If the spring constant is 100 N/m, how much potential energy is stored in the spring?

  1. 0.5 J

  2. 1 J

  3. 1.5 J

  4. 2 J
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Potential energy stored in a spring = (1/2)kx², where k is the spring constant and x is the displacement from equilibrium.