Tag: oscillations due to a spring

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Questions Related to oscillations due to a spring

Multiple choice physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

A spring of force constant k is cut into 4 equal parts. The spring constant of each piece become_______ times and time period will become______ times.

  1. [5, 1/2]

  2. [4, 1/2]

  3. [7, 1/2]

  4. [4, 1/3]
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cutting a spring into 4 equal parts makes the spring constant of each piece 4k. The time period T = 2 * pi * sqrt(m/k). Since k becomes 4k, the new time period T' = 2 * pi * sqrt(m/4k) = T/2.

Multiple choice physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

When two blocks connected by a spring move towards each other under mutual interaction:

  1. Their velocities are equal and opposite

  2. Their accelerations are equal and opposite

  3. The forces acting on them are equal and opposite

  4. Their momenta are equal and opposite.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If we take the two blocks plus spring as the system there is no external force acting on this system.
The accelerations will be equal and opposite if masses are equal. Since the forces are internal, they will be equal and opposite.

Multiple choice physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

Two springs have their force constants ${ K } _ { 1 }$ and ${ K } _ { 2 }.$ Both are stretched till their elastic energies are equal. Then,ratio of stretching forces ${ K } _ { 1 } / { K } _ { 2 }$ is equal to:

  1. $K _ { 1 } / K _ { 2 }$
  2. $\mathbf { K } _ { 2 } : \mathbf { K } _ { 1 }$
  3. $\sqrt { K _ { 1 } } : \sqrt { K _ { 2 } }$
  4. $\mathbf { K } _ { 2 } ^ { 2 } : \mathbf { K } _ { 2 } ^ { 2 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Elastic energy U = F^2 / (2k). If U1 = U2, then F1^2 / (2k1) = F2^2 / (2k2). Rearranging gives (F1/F2)^2 = k1/k2, so F1/F2 = sqrt(k1)/sqrt(k2).

Multiple choice physics simple harmonic motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

A mass of 2 kg falls from a height of 40 cm, on a spring with a force constant of 1960 N/m. The spring is compressed by ? (Take $g=9.8m/s^2$)

  1. 9 cm

  2. 1.0 cm

  3. 20 cm

  4. 5 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using conservation of energy: m * g * (h + x) = 1/2 * k * x^2. Plugging in m=2, g=9.8, h=0.4, k=1960 results in a quadratic equation for compression x. Solving this yields x = 0.09m or 9cm.

Multiple choice physics simple harmonic motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

A string fixed at both ends vibrates in a resonant mode with separation of $6.0$cm between the consecutive nodes. For the next to next higher resonant frequency this separation is reduced by $2.0$cm. The length of the spring is 

  1. 8 cm

  2. 16 cm

  3. 24 cm

  4. 32 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The separation between consecutive nodes in a standing wave is half the wavelength (lambda/2 = 6 cm, so lambda = 12 cm). For the next to next higher resonant frequency, the node separation decreases by 2 cm to 4 cm (lambda_new/2 = 4 cm, so lambda_new = 8 cm). By analyzing harmonic conditions, the length of the string is 24 cm.

Multiple choice physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

One end of a light spring of force constant K is fixed to ceiling the other end is fixed to block of mass M initially the spring is relaxed the work done by the external agent to lower the Hanging body of mass M slowly till it comes to equilibrium is

  1. $3 m^2 g^2/ 2k$
  2. $m^2 g^2/ 2k$
  3. $-3 m^2 g^2/ 2k$
  4. $- m^2 g^2/ 2k$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

A spring oscillates with frequency $1$ cycle per second. What approximate length must a simple pendulum have to oscillate with that same frequency?

  1. 25 cm

  2. 50 cm

  3. 67 cm

  4. 90 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A spring with frequency f = 1 Hz has a period T = 1 s. A simple pendulum having the same frequency must have length L given by T = 2*pi*sqrt(L/g). Setting T = 1 s and g = 9.8 or pi^2 gives L = g / (4*pi^2) approximately equal to 0.25 meters, or 25 cm.

Multiple choice physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

Two identical springs are fixed at one end and masses $1$ $kg$ and $4$ $kg$ are suspended at their other ends. They are both stretched down from their mean position and let go simultaneously. If they are in the same phase after every $4$ seconds then the springs constant $k$ is 

  1. $\pi \dfrac { N }{ m } $
  2. ${ \pi }^{ 2 }\dfrac { N }{ m } $
  3. $2\pi \dfrac { N }{ m } $
  4. $given$ $data$ $is$ $insufficient$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The time periods are T1 = 2*pi*sqrt(1/k) and T2 = 2*pi*sqrt(4/k) = 2*T1. They are in the same phase after every 4 seconds, meaning 4 seconds is a common multiple of their periods. Solving the relations yields the spring constant k in terms of pi squared.

Multiple choice physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

A body is attached to the lower end of a vertical spiral spring and it is gradually lowered to its equilibrium position.This stretches the spring by a length d.If the same body attached to the same spring is allowed to fall suddenly, what would be the maximum stretching in this case?

  1. d

  2. 2d

  3. 3d

  4. 1/2d
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Gradual lowering reaches equilibrium at d = mg/k. Sudden release results in maximum extension at 2d because the potential energy lost by the mass (mg * 2d) equals the energy stored in the spring (1/2 * k * (2d)^2).

Multiple choice physics oscillatory motion motion of a mass suspended by two springs example of simple harmonic motion oscillations due to a spring

A spring $40\ mm$ long is stretched by the application of a force. If $10\ N$ force required to stretch the spring through $1\ mm$, then work done in stretching the spring through $40\ mm$ is:

  1. 84 J

  2. 68 J

  3. 23 J

  4. 8 J
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Force constant k = F/x = 10N / 1mm = 10,000 N/m. Work done W = 1/2 * k * x^2 = 0.5 * 10,000 * (0.04m)^2 = 5,000 * 0.0016 = 8 J.