Tag: oscillations

Questions Related to oscillations

Two equal masses are connected by a spring satisfying Hooks law and are placed on a frictionless table. The spring is elongated a little and allowed to go. Let the angular frequency of oscillations be $\omega$. Now one of the masses is stopped. The square of the new angular frequency is :

horizontal oscillations of a mass attached to a spring oscillations due to a spring simple harmonic motion oscillations physics

  1. ${\omega}^{2}$

  2. $\dfrac{{\omega}^{2}}{2}$

  3. $\dfrac{{\omega}^{2}}{3}$

  4. $2{\omega}^{2}$

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Correct Option: B

The springs of force constants $K, 2K, 4K, 8K,....128K$ are connected vertically in series and a body of mass M is suspended from the last spring. If this system is set into oscillations, the time period will be- 

horizontal oscillations of a mass attached to a spring oscillations due to a spring simple harmonic motion oscillations physics

  1. $2\pi \sqrt{\dfrac{2K}{M}}$

  2. $2\pi \sqrt{\dfrac{M}{K}}$

  3. $2\pi \sqrt{\dfrac{2M}{K}}$

  4. $2\pi \sqrt{\dfrac{M}{2K}}$

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Correct Option: C

A spring is placed in vertical position by suspending it from a hook at its top. A similar hook on the bottom of the spring is at $11\ cm$ above a table top. A mass of $75\ g$ and of negligible size is then suspended from the bottom hook, which is measured to be $4.5\ cm$ above the table top. The mass is then pulled down a distance of $4\ cm$ and released. Find the approximate position of the bottom hook after $s$?
Take $g=10m/{s}^{2}$ and hooks mass to be negligible.

horizontal oscillations of a mass attached to a spring oscillations due to a spring simple harmonic motion oscillations physics

  1. $5cm$ above the table top

  2. $4.5cm$ above the table top

  3. $9cm$ above the table top

  4. $0.5cm$ above the table top

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Correct Option: A

A block of mass m moving with speed v compresses a spring through distance X before its speed is halved.What is the value of spring constant?

horizontal oscillations of a mass attached to a spring oscillations due to a spring simple harmonic motion oscillations physics

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

  2. $\frac{{m{v^2}}}{{4{x^2}}}$

  3. $\frac{{m{v^2}}}{{2{x^2}}}$

  4. $\frac{{2m{v^2}}}{{{x^2}}}$

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Correct Option: A

A spring executes SHM with mass of 10 kg attached to it. The force constant of spring is 10 N/m.If at any instant its velocity is 40 cm/sec. The displacement will be (here amplitude is0.5m) 

horizontal oscillations of a mass attached to a spring oscillations due to a spring simple harmonic motion oscillations physics

  1. 0.06 m

  2. 0.3 m

  3. 0.01 m

  4. 1.0 m

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Correct Option: B

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

horizontal oscillations of a mass attached to a spring oscillations due to a spring simple harmonic motion oscillations physics

  1. $\pi \frac { N } { m }$

  2. $\pi ^ { 2 } \frac { \mathrm { N } } { \mathrm { m } }$

  3. 2$\pi \frac { \mathrm { N } } { \mathrm { m } }$

  4. given data is insufficient

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Correct Option: A

A spring mass system is hanging from the ceiling of an elevator in equilibrium. The elevator suddenly starts accelerating upwards with accelerating a, consider all the options in the reference frame of elevator. 

horizontal oscillations of a mass attached to a spring oscillations due to a spring simple harmonic motion oscillations physics

  1. the frequency of oscillation is $\dfrac { 1 }{ 2\pi } \sqrt { \dfrac { k }{ m } } $

  2. the amplitude of the resulting SHM is $\dfrac { ma }{ k } $

  3. amplitude of resulting SHM is $\dfrac { m\left( g+a \right) }{ k } $

  4. maximum speed of block during oscillation is $\left( \sqrt { \dfrac { m }{ k } } \right) a$

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Correct Option: B
Explanation:

Frequency =$2 \pi(m/k)$ frequecy  is independent of $g$ in spring

Extension in spring in equilibrium
initial $ = \dfrac{{mg}}{k}$
Extension in spring in equilibrium  in accelerating lift $m(g+a)$
Amplitude $ = \dfrac{{m\left( {g + a} \right)}}{k} - \dfrac{{mg}}{k} = \dfrac{{ma}}{k}$ 

The reading of a spring balance when a block is suspended from it in air is $60 N$. The reading is changed to $40 N$ when the block is submerged in water. The specific gravity of the block must be therefore.

horizontal oscillations of a mass attached to a spring oscillations due to a spring simple harmonic motion oscillations physics

  1. 3/2

  2. 6

  3. 2

  4. 3

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Correct Option: D

A block of mass $1$ kg is connected to a spring of spring constant $\pi^2 N/m$ fixed at other end and kept on smooth level ground. The block is pulled by a distance of $1$ cm from natural length position and released. After what time does the block compress the spring by $\frac{1}{2} cm$.

horizontal oscillations of a mass attached to a spring oscillations due to a spring simple harmonic motion oscillations physics

  1. $\dfrac{2}{3}$ sec

  2. $\dfrac{1}{3}$ sec

  3. $\dfrac{1}{6}$ sec

  4. $\dfrac{1}{12}$ sec

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Correct Option: C

A spring (of spring constant $= k )$ is cut into 4 equal parts and two parts are connected in parallel. What is the effective spring constant of these parts?

horizontal oscillations of a mass attached to a spring oscillations due to a spring simple harmonic motion oscillations physics

  1. $4K$

  2. $16K$

  3. $8K$

  4. $6K$

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Correct Option: C