Tag: oscillations

Quizzes (16) Questions (206)

Questions Related to oscillations

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

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$\ m/s^2$)

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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

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

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

  1. 0.5 N

  2. 1 N

  3. 2 N

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

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

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

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.

  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

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

Speed v of a particle moving along a straight line, when it is at a distance x from a fixed point on the line is given by $V^2=108-9x^2$(all quantities in S. I. unit). Then

  1. The motion is uniformly accelerated along the straight line
  2. The magnitude of the acceleration at a distance 3 cm from the fixed point is $0.27m/s^2$
  3. The motion is simple harmonic about $x=6$m

  4. The maximum displacement from fixed point is 4cm.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$V^2=108-9x^2$


for SHM

$V^2=\omega^2(A^2-X^2)$

$V^2=9(12-X^2)$

$W=3,A=2\sqrt{3}$

$v\dfrac{dv}{dx}=9(12-2X)$

$\dfrac{dV}{dX}=0$ at $X=6$

So, it will perform SHM about $X=6m$

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

A planck with a body of mass m placed on to it starts moving straight up with the law $y=a(1-\cos{\omega t})$ where $\omega$ is displacement. Find the time dependent force:

  1. $-ma\omega^2\cos{\omega t}$
  2. $ma\omega^2\cos{\omega t}$
  3. $ma\omega^2\sin{\omega t}$
  4. $mg+ma\omega^2\cos{\omega t}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total force on the particle will be
$F=mg+m\dfrac { d^{ 2 }y }{ dt^{ 2 } } $
since $y=a(1-\cos { \omega t } )\\ \Rightarrow \dfrac { dy }{ dt } =a\omega \sin { \omega t } \\ \Rightarrow \dfrac { d^{ 2 }y }{ dt^{ 2 } } =a\omega ^{ 2 }\cos { \omega t } $
$\Rightarrow F=mg+ma\omega ^{ 2 }\cos { \omega t } $