Tag: simple harmonic motion

Questions Related to simple harmonic motion

A bob of mass  $\mathrm { M }$  is hung using a string of length  $\mathrm { l }.$  A mass  $m$  moving with a velocity  $u$  pierces through the bob and emerges out with velocity  $\dfrac { u } { 3 } ,$  The frequency of oscillation of the bob considering as amplitude  $A$ is

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

  1. $2 \pi \sqrt { \dfrac { 3 m u } { 2 M A } }$

  2. $\dfrac { 1 } { 2 \pi } \sqrt { \dfrac { 2 m } { 3 M A } }$

  3. $\dfrac { 1 } { 2 \pi } \left( \dfrac { 2 m u } { 3 M A } \right)$

  4. cannot be found

Show answer
Correct Option: A

A  body of mass 0.98 Kg is suspended from a spring of spring constant K = 2N/m. Then the period is. 

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

  1. 4.9s

  2. 4.4s

  3. 5.2s

  4. None

Show answer
Correct Option: B

Two particles  $A$  and  $B$  of equal masses are suspended from two massless springs of spring constants  $k _ { 1 }$  and  $k _ { 2 }$  respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitudes of  $A$  and  $B$  is

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

  1. $\sqrt { k _ { 1 } / k _ { 2 } }$

  2. $k _ { 1 } / k _ { 2 }$

  3. $\sqrt { k _ { 2 } / k _ { 1 } }$

  4. $k _ { 2 } / k _ { 1 }$

Show answer
Correct Option: C

A block of mass m is suspended separately by two different spring have time period $ t _1 and t _2 $ . if same mass is connected to parallel combination of both springs , then its time period is given by

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

  1. $ \dfrac {t _1t _2}{t _1 +t _2} $

  2. $ \dfrac {t _1t _2}{\sqrt {t^2 _1+ t^2 _1} } $

  3. $ \sqrt {\dfrac { t _1t _2}{ t _1 +t _2}} $

  4. $\sqrt {(t _1)^2 + (t _2)^2} $

Show answer
Correct Option: D

Frequency of a block in spring-mass system is $\displaystyle \upsilon $, if it is taken in a lift slowly accelerating upward, then frequency will 

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

  1. decrease

  2. increase

  3. remain constant

  4. none

Show answer
Correct Option: C
Explanation:

$\omega=2\pi\sqrt{\dfrac{K}{M}}$

Frequency is independent of gravity
Hence it will remain constant

A $1.5$ kg block at rest on a tabletop is attached to a horizontal spring having a spring constant of $19.6$ N/m. The spring is initially unstretched. A constant $20.0$ N horizontal force is applied to the object causing the spring to stretch.Determine the speed of the block after it has moved $0.30$ m from equilibrium if the surface between the block and the tabletop is frictionless.

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

  1. $2.61\ m/s$

  2. $3.61\ m/s$

  3. $7.61\ m/s$

  4. $8.1\ m/s$

Show answer
Correct Option: B
Explanation:

This system will exhibits S.H.M with angular frequency $\omega =\sqrt { \cfrac { k }{ m }  } =\sqrt { \cfrac { 19.6 }{ 1.5 }  } $

$k$= spring constant 
$m$= mass of the body
The string stretched by the maximum A restoring force at maximum stretch= force acting on body
$\Rightarrow kA=F$
$\Rightarrow A=\cfrac { F }{ k } =\cfrac { 20 }{ 19.6 } $
$F=20N$
$K=19.6\quad N/m$
Now if x is displacement from mean position, the velocity is given by:
$v=\omega =\sqrt { ({ A }^{ 2 }-{ x }^{ 2 }) } $
$v=\omega =\sqrt { \cfrac { 19.6 }{ 1.5 } ({ \cfrac { 20 }{ 19.6 }  }^{ 2 }-{ 0.3 }^{ 2 }) } $
$=3.523m/s$

A body of mass $m$ is suspended from a spring of spring constant $k$. A damping force proportional to the velocity exerts itself on the mass. An appropriate representation of the motion is 

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

  1. $ m \dfrac{d^2x}{dt^2} - c \dfrac{dx}{dt} + kx = 0$

  2. $ m \dfrac{d^2x}{dt^2} + c \dfrac{dx}{dt} - kx = 0$

  3. $ m \dfrac{d^2x}{dt^2} - c \dfrac{dx}{dt} - kx = 0$

  4. $ m \dfrac{d^2x}{dt^2} + c \dfrac{dx}{dt} + kx = 0$

Show answer
Correct Option: D
Explanation:
The forces on the mass $m$ are due to spring and damper.

Suppose the mass moves by a distance $x$ from equilibrium and travels with a velocity $\displaystyle \frac{dx}{dt}$, then

Force due to spring is $-kx$ and force due to damper is $\displaystyle -c\frac{dx}{dt}$

By Newton's Second Law of motion, we have $m\displaystyle \frac{d^2x}{dt^2} = -kx-c\frac{dx}{dt}$

Thus, the equation of motion is $\displaystyle m\frac{d^2x}{dt^2}+c\frac{dx}{dt}+kx=0$

A body of mass $m$ attached to the spring experiences a drag force proportional to its velocity and an external force $F(t) = F _o \cos \omega _ot$. The position of the mass at any point in time can be given by:

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

  1. $x(t) = c _1 \sin (\omega t + \phi) + (\dfrac{F _o}{\omega ^2 - \omega _o ^2}) \cos \omega _o t$

  2. $x(t) = c _1 \cos (\omega t + \phi) + (\dfrac{F _o}{\omega ^2 - \omega _o ^2}) \cos \omega _o t$

  3. $x(t) = c _1 \sin (\omega t) + (\dfrac{F _o}{\omega ^2 - \omega _o ^2}) \cos \omega _o t$

  4. $x(t) = c _1 \cos (\omega t) + (\dfrac{F _o}{\omega ^2 - \omega _o ^2}) \cos \omega _o t$

Show answer
Correct Option: A,B,C,D
Explanation:

Initially, we already know that the displacement at any moment (Instant) of time for spring mass system is:

$x=a\sin { (\omega t+\phi ) } $ or,
$x=a\cos { (\omega t+\phi ) } $
And here an external force is experienced thus, all the four options give position at any time.

The natural angular frequency of a particle of mass 'm' attached to an ideal spring of force constant 'K' is

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

  1. $\sqrt{\frac{K}{m}}$

  2. $\sqrt{\frac{m}{K}}$

  3. $\left ( \frac{K}{m} \right )^{2}$

  4. $\left ( \frac{m}{K} \right )^{2}$

Show answer
Correct Option: A
Explanation:
Suppose you displace the particle by a distance $'x'$
The spring now exerts a force,
This provides nccenary force for $SHM$
$\Rightarrow \ F=mwe^2x=k2$ ($w:$ natural angular frequency )
$\Rightarrow \ w=\sqrt {K/m}$

Spring in vehicles are introduces to:

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

  1. Reduce

  2. Reduce impluse

  3. Reduce force

  4. Reduce velocity

Show answer
Correct Option: A