Tag: oscillations

Questions Related to oscillations

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

force in shm oscillations oscillation and waves physics

  1. Acceleration =$-k _0x+k _1x^2$

  2. Acceleration =$-k(x+a)$

  3. Acceleration =$k(x+a)$

  4. Acceleration =$kx$

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Correct Option: B

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

force in shm oscillations oscillation and waves physics

  1. 4 dynes/cm

  2. 4 N/cm

  3. 4 N/m

  4. 4 dynes/m

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Correct Option: A
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

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 :

force in shm oscillations oscillation and waves physics

  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

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Correct Option: A
Explanation:

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

In case of force oscillations of a body

force in shm oscillations oscillation and waves physics

  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.

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Correct Option: C
Explanation:

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

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.

force in shm oscillations oscillation and waves physics

  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

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Correct Option: A
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.

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 

force in shm oscillations oscillation and waves physics

  1. 8 kW

  2. 16 kW

  3. 32kw

  4. 76kw

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Correct Option: C
Explanation:
Here $F\propto V^{2}$
$P = F\times V$
$\propto V^{2}\times V = V^{3}$
$\therefore \dfrac{P _{1}}{P _{2}}=\dfrac{V _{1}^{3}}{V _{2}^{3}}=\left(\dfrac{V}{2V}\right)^{3}=\dfrac{1}{8}$
$\therefore P _{1}=4kw$
$P _{2}=8\times 4= 32kw$
$\therefore P _{2}= 32kw$

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:

force in shm oscillations oscillation and waves physics

  1. $ 6 $ N

  2. $9$ N

  3. $4$ N

  4. $\sqrt{6} $ N

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Correct Option: B
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$

Restoring force in the SHM is

force in shm oscillations oscillation and waves physics

  1. conservative

  2. nonconservative

  3. frictional

  4. centripetal

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Correct Option: A
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.

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.

force in shm oscillations oscillation and waves physics

  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. $\overset{\rightarrow}{a}.\overset{\rightarrow}{x}<0$

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Correct Option: C
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, $F=ma\Rightarrow ma\times a=0$.

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 $F$.

force in shm oscillations oscillation and waves physics

  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.

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Correct Option: A