Tag: example of simple harmonic motion

Questions Related to example of simple harmonic motion

An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is 15 ${ cms }^{ -1 }$ and the period is 628 milli-seconds. The amplitude of the motion in centimeters is :

physics oscillatory motion a few applications of linear shm simple pendulum example of simple harmonic motion

  1. 3.0

  2. 2.0

  3. 1.5

  4. 1.0

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Correct Option: C
Explanation:

Given,


$T=628ms=0.628s$


$v _{max}=15cm/s=0.15m/s$

The maximum speed of the object is given by

$v _{max}=A\omega=A\dfrac{2\pi}{T}$

Amplitude, $A=\dfrac{v _{max}T}{2\pi}$

$A=\dfrac{0.15\times 0.628}{2\times 3.14}=0.015 m$

$A=1.5cm$

The correct option is C.

The different equation for linear SHM of a partial of mass $2g$ is $\dfrac {d^{2}x}{dt^{2}} + 16x = 0$. Find the force constant. $[K = mw^{2}]$.

physics oscillations a few applications of linear shm simple pendulum example of simple harmonic motion

  1. $0.02\ N/m$.

  2. $0.032\ N/m$.

  3. $0.132\ N/m$.

  4. $0.232\ N/m$.

Show answer
Correct Option: B

If a body mass $36 gm$ moves with S,H,M of amplitude $A=13$ and period  $T=12 sec$. At a time $t=0$ the displacement is $x=+13 cm$. The shortest time of passage from $x=+6.5$ cm to $x=-6.5$ is

physics oscillatory motion a few applications of linear shm simple pendulum example of simple harmonic motion

  1. 4 sec

  2. 2 sec

  3. 6 sec

  4. 3 sec

Show answer
Correct Option: B
Explanation:

$\begin{array}{l} m=3bg,\, A=13,T=125 \ displacementx\left( t \right) =13\sin  \left( { \frac { { 2\pi t } }{ T }  } \right)  \end{array}$

Shortest time is at maximum slope which crosses zero. It will be from $ - 6.5\,\,to\,\,6.5\,\,$ or 2 times from $0\,to\,\,6.5$
$\begin{array}{l} 6.5=13\sin  \left( { \frac { { 2\pi t } }{ { 12 } }  } \right)  \ 0.5=\sin  \left[ { \left( { \frac { \pi  }{ 6 }  } \right) t } \right]  \ t=1\, \sec   \ total\, \, time=\, 2\times 1=2 \end{array}$

A function of time given by $\left(\sin{\omega t}-\cos{\omega t}\right)$ represents

physics oscillatory motion a few applications of linear shm simple pendulum example of simple harmonic motion

  1. simple harmonic motion

  2. non-periodic motion

  3. periodic but not simple harmonic motion

  4. oscillatory but not simple harmonic motion

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Correct Option: A
Explanation:

$\begin{array}{l} \sin  \omega t-\cos  \omega t \ =\sqrt { 2 } \left[ { \frac { 1 }{ { \sqrt { 2 }  } } \sin  \omega t-\frac { 1 }{ { \sqrt { 2 }  } } \cos  \omega t } \right]  \ =\sqrt { 2 } \left[ { \sin  \omega t\times \cos  \frac { \pi  }{ 4 } -\cos  \omega t\times \sin  \frac { \pi  }{ 4 }  } \right]  \ =\sqrt { 2 } \sin  \left( { \omega t-\frac { \pi  }{ 4 }  } \right)  \ this\, \, function\, \, represents\, \, SHM\, \, as\, \, it\, \, can\, \, be\, \, written\, \, in\, \, the\, \, form: \ a\sin  \left( { \omega t+\phi  } \right)  \ its\, \, period\, \, is,\, \, \frac { { 2\pi  } }{ \omega  }  \end{array}$

Hence,
option $(A)$ is correct answer.

A particle is subjected to two simple harmonic motions along $x$ and $y$ directions according to $x=3\sin\ 100\pi t$ $y=4\sin\ 100\pi t$

physics oscillatory motion a few applications of linear shm simple pendulum example of simple harmonic motion

  1. Motion of particle will be on ellipse travelling in clockwise direction.

  2. Motion of particle will be on a straight line with slope $4/3$

  3. Motion will be simple harmonic motion with amplitude $5$.

  4. Phase difference between two motions is $\pi/2$.

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Correct Option: A

A ring whose diameter is 1 meter, oscillates simple harmonically in a vertical plane about a nail fixed at its circumference and perpendicular to plane of ring. The time period will be

physics oscillatory motion a few applications of linear shm simple pendulum example of simple harmonic motion

  1. 1/4 sec

  2. 1/2 sec

  3. 2sec

  4. None of these

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Correct Option: C

The graph between restoring force and time in case of SHM is a

physics oscillations a few applications of linear shm simple pendulum example of simple harmonic motion

  1. parabola

  2. sine curve

  3. straight line

  4. circle

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Correct Option: B
Explanation:

We know that for SHM, $x=A\sin(\omega t + \theta)$ and $F=kx=kA\sin(\omega t + \theta)$
Thus it's a sine curve.

A person weighing $60\ kg$ stands on a platform which oscillates up and down at a frequency of $2\ Hz$ and amplitude $5\ cm$. The maximum and minimum apparent weights are nearly: ($g$ = 10$\ m/s^2$)

physics oscillations a few applications of linear shm simple pendulum example of simple harmonic motion

  1. $108$ kg-wt, $12$ kg-wt

  2. $108$ kg-wt, $24$ kg-wt

  3. $54$ kg-wt, $12$ kg-wt

  4. $54$ kg-wt, $24$ kg-wt

Show answer
Correct Option: A
Explanation:

$a=\omega^{2}x$
So, $a _{max}=$ $\omega^{2}A$
We know that $\omega=2\pi  f$
So, $a _{max}=\dfrac{(2\pi\times 2)^{2}\times 5}{100}$
Case I:
$N-mg=ma _{max}$
$N=m(a _{max}+g)$
$=60(10+\dfrac{16\times \pi^{2}\times 5}{100})$
$=1080 $ 

$ N=108$ kg-wt

Case II:
$mg-N=ma _{max}$
or, $N=mg-ma _{max}$
$=60(10-8)$
$=120\ N=12$ kg-wt

A body of mass $0.5$ kg is performing S.H.M. with a time period $\pi /2$ seconds. If its velocity at mean position is $1$ m/s, the restoring force acts on the body at a phase angle $60^o$ from extreme position is

physics oscillations a few applications of linear shm simple pendulum example of simple harmonic motion

  1. 0.5 N

  2. 1 N

  3. 2 N

  4. 4 N

Show answer
Correct Option: B
Explanation:

$T=\dfrac{ \pi}{2}$
$V _{max}=1 m/sec$
$\omega =\dfrac{2\pi}{T}$
$V=4  rad/sec$
$V _{max=}A\omega$
$A\times 4=1$
$A=\dfrac {1}{4}$
$a=\omega^{2}x$
$F= m\omega^{2}x$
$x=A   cos   60^o$
$\therefore x=\dfrac {A}{2}$
$F=0.5\times (4)^{2}\times \dfrac {1}{4}\times \dfrac{1}{2}$
$F=1N$

Assertion : If a block is in SHM, and a new constant force acts in the direction of change, the mean position may change.
Reason :In SHM only variable forces should act on the body, for example spring force.

physics oscillations a few applications of linear shm simple pendulum example of simple harmonic motion

  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

  2. Both Assertion and Reason are correct and Reason is not  the correct explanation for Assertion

  3. Assertion is correct and Reason is incorrect 

  4. Assertion is incorrect and Reason is correct 

Show answer
Correct Option: C
Explanation:

In SHM a constant force brings no effective change in the motion but the mean position accelerates.