Tag: oscillations

Quizzes (16) Questions (206)

Questions Related to oscillations

Multiple choice force in shm oscillations oscillation and waves physics

Which one of the following equations of motion represents simple harmonic motion?

  1. Acceleration =$-k _0x+k _1x^2$
  2. Acceleration =$-k(x+a)$
  3. Acceleration =$k(x+a)$
  4. Acceleration =$kx$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple harmonic motion (SHM) is defined by a restoring force (or acceleration) that is directly proportional to the negative displacement from the equilibrium position, expressed as a = -kx. Option B represents this form, where the equilibrium position is shifted by 'a'.

Multiple choice force in shm oscillations oscillation and waves physics

The mass of particle executing S.H.M is 1 gm.If its periodic time is $\pi $ seconds, the value of force constant is:-

  1. 4 dynes/cm

  2. 4 N/cm

  3. 4 N/m

  4. 4 dynes/m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, mass $m=1 gm$; time period $T=\pi$ sec

The angular frequency $\omega=\frac{2\pi}{T}=\frac{2\pi}{\pi}=2$
As $\omega=\sqrt{k/m}$  where ($k$ is the force constant),
$k=m\omega^2=(1 gm)(2)^2=4$ dynes/cm

Multiple choice force in shm oscillations oscillation and waves physics

A particle of mass 1kg is moving in a S.H.M with an amplitude of 0.02m and a frequency of 60Hz. The maximum force acting on the particle is :

  1. $2.88 \times 10^{3}$N
  2. $1.44 \times 10^{3}$N
  3. $5.67 \times 10^{3}$N
  4. $0.75 \times 10^{3}$N
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$f = 60\ Hz$
$w = 2\pi f = 120\pi \  rad/sec$
$F = mw^{2}A$
$= 1 \ kg \times 14400 \times \pi ^{2} \times  0.02$
$= 2.88 \times 10^{3}N$

Multiple choice force in shm oscillations oscillation and waves physics

In case of force oscillations of a body

  1. driving force is constant throughout.

  2. driving force is to be applied only momentarily.

  3. driving force has to be periodic and continuous.

  4. driving force is not required.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In case of force oscillations of a body driving force has to be periodic and continuous.

Multiple choice force in shm oscillations oscillation and waves physics

A student says that he had applied a force $F= -k\sqrt {x}$ on a particle and the particle moves in simple harmonic motion. He refuses to tell whether $k$ is a constant or not. Assume that he has worked only with positive $x$ and no other force acted on the particle.

  1. As $x$ increases $k$ increases
  2. As $x$ increases $k$ decreases
  3. As $x$ increases $k$ remains constant

  4. The motion cannot be simple harmonic
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given that the motion of the particle is Simple Harmonic Motion.

$F=-m\omega^2 x$

The force applied by the student is given by, 

$F=-\dfrac{-k}{x}$

If the motion is S.H.M., then both will be equal.

So,

$\dfrac{-k}{-x}=m\omega^2 x$

$k=m\omega^2 x^2$

This means, if $x$ increases, then $k$ also increases.

So the correct answer is option a.
Multiple choice force in shm oscillations oscillation and waves physics

The force of a required to row a boat at velocity is proportional to square of its speed of v km/ h requires 4 KW, how many does a seepd of 2V km/h required 

  1. 8 kW

  2. 16 kW

  3. 32kw

  4. 76kw
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Here $F\propto V^{2}$
$P = F\times V$
$\propto V^{2}\times V = V^{3}$
$\therefore \dfrac{P _{1}}{P _{2}}=\dfrac{V _{1}^{3}}{V _{2}^{3}}=\left(\dfrac{V}{2V}\right)^{3}=\dfrac{1}{8}$
$\therefore P _{1}=4kw$
$P _{2}=8\times 4= 32kw$
$\therefore P _{2}= 32kw$
Multiple choice force in shm oscillations oscillation and waves physics

A body is executing SHM. If the force acting on the body is 6N when the displacement is 2 cm, then the force acting on the body when the displacement is 3 cm in newton is:

  1. $ 6 $ N
  2. $9$ N
  3. $4$ N
  4. $\sqrt{6} $ N
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$ F = m w^{2}x$
$ \dfrac{F _{1}}{F _{2}} = \dfrac{x _{1}}{x _{2}}$
$ F _{2}  = \dfrac{3}{2}\times 6 \ N  =  9 \ N$
Multiple choice force in shm oscillations oscillation and waves physics

Restoring force in the SHM is

  1. conservative

  2. nonconservative

  3. frictional

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

A conservative force is a force with the property that the work done in moving a particle between two points is independent of the taken path. Restoring force $F=kx,$ is such kind of force and is conservative.

Multiple choice force in shm oscillations oscillation and waves physics

In SHM, select the wrong statement, where ${F}$ is the force, ${a}$ is the acceleration and ${v}$ is the velocity of the particle in SHM.

  1. $\overset{\rightarrow}{F}\times \overset{\rightarrow}{v}$ is a null vector
  2. $|\overset{\rightarrow}{F}\times \overset{\rightarrow}{a}|=0$ (always)
  3. $\overset{\rightarrow}{F}\times \overset{\rightarrow}{a}< {0}$
  4. $\overset{\rightarrow}{a}.\overset{\rightarrow}{x}<0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The velocity, acceleration and thus the force are along the direction of motion in the SHM.

So the cross product of Force with velocity or acceleration is always zero.
Thus $A$ and $B$ are correct.
Also, acceleration is always in opposite direction to the displacement vector. So dot-product of acceleration and displacement is always negative. Thus $D$ is also correct.
$C$ is the wrong statement as the cross product of force and acceleration is strictly zero, because, $F=ma\Rightarrow ma\times a=0$.

Multiple choice force in shm oscillations oscillation and waves physics

A coin is placed on a horizontal platform, which undergoes horizontal simple harmonic motion about a mean position $O$.The coin does not slip on the platform. The force of friction acting on the coin is $F$.

  1. $F$ is always directed towards $O$
  2. $F$ is directed towards $O$ when the coin is moving away from $O$, and away from $O$ when the coin moves towards $O$
  3. $F=0$ when the coin and platform come to rest momentarily at the extreme position of the harmonic motion.
  4. $F$ is maximum when the coin and platform come to rest momentarily at the extreme position of the harmonic motion.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In horizontal SHM, the platform accelerates towards the mean position O. To prevent slipping, the static friction force must provide this acceleration, meaning the friction force must always be directed towards O.