Tag: oscillatory motion

Questions Related to oscillatory motion

The pendulum of a certain clock has time period $2.04 s$. How fast or slow does the clock run during $24$ hour?

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $28.8$ minutes slow

  2. $28.8$ minutes fast

  3. $14.4$ minutes fast

  4. $14.4$ minutes slow

Show answer
Correct Option: A

A string of simple pendulum can bear maximum tension that is twice the weight of the bob. What is the maximum angle $(\theta)$ with which it can oscillate?

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $0^0$

  2. $45^0$

  3. $60^0$

  4. $90^0$

Show answer
Correct Option: B

A bob is suspended from an ideal string of length $l$. Now it is pulled to a side through $60^{o}$ to vertical and rotates along a horizontal circle. Then its period of revolution is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $ 2\pi \sqrt{ l/g }$

  2. $ \pi \sqrt{ l/2g }$

  3. $\pi\sqrt{ 2l/g }$

  4. $\pi\sqrt{ l/g }$

Show answer
Correct Option: C

Two simple pendulums have time period $4\ s$ and $5\ s$ respectively. If they started simultaneously from the mean positive in the same direction, then the phase difference between them by the time the larger one completes one osicillation is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $\dfrac {\pi}{6}$

  2. $\dfrac {\pi}{3}$

  3. $\dfrac {\pi}{2}$

  4. $\dfrac {\pi}{4}$

Show answer
Correct Option: A

Write the torque equation for the bob of a pendulum if it makes an angle of $\theta$ with the vertical and I is the moment of inertia of the bob w.r.t the point of suspension

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $I \dfrac{d^2 \theta}{dt^2}=mgL \cos \theta$

  2. $I \dfrac{d^2 \theta}{dt^2}=mgL \sin \theta$

  3. $I \dfrac{d^2 \theta}{dt^2}=mgL \tan \theta$

  4. $I \dfrac{d^2 \theta}{dt^2}=mg \sin \theta$

Show answer
Correct Option: B
Explanation:

Taking the torque about the point of suspension, we can write $I \dfrac{d^2 \theta}{dt^2}=mgL \sin \theta$

The correct option is (b)

One end of spring of spring constant k is attached to the centre of a disc of mass m and radius R and the other end of the spring connected to a rigid wall. A string is wrapped on the disc and the end A of the string is pulled through a distance a and then released.
The disc is placed on a horizontal rough surface and there is no slipping at any contact point What is the amplitude of the oscillation of the centre of the disc?

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. a

  2. 2a

  3. a/2

  4. none of these.

Show answer
Correct Option: C
Explanation:

Displacement of the topmost point of the disc = a.
Disc undergoes rolling without slipping.
Hence the displacement of the centre of the disc = a/2
Thus the amplitude of the oscillation of the centre of the disc = a/2
Hence (C) is correct.

The angular frequency of a torsional pendulum is $\omega$ rad/s. If the moment of inertia of the object is I, the torsional constant of the wire is related to the rotational kinetic energy of the disc, if the disc was rotating with an angular velocity $\omega$ is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. k= 2 KE

  2. k= KE

  3. k= 4 KE

  4. k= KE/2

Show answer
Correct Option: A
Explanation:

we know that $T=2 \pi \sqrt{I/k}$. Substituting the values given, we get, $k= I \omega^2 =2 \times $ kinetic energy

The correct option is (a)

A small sphere is suspended by a string from the ceiling of a car. If the car begins to move with a constant acceleration $a$, the inclination of the string with the vertical is:-

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. ${\tan ^{ - 1}}\left( {\dfrac{1}{2}} \right)$ in the direction of motion

  2. ${\tan ^{ - 1}}\left( {\dfrac{1}{2}} \right)$ opposite to the direction of motion

  3. ${\tan ^{ - 1}}\left( 2 \right)$ in the direction of motion

  4. ${\tan ^{ - 1}}\left( 2 \right)$ opposite to the direction of motion

Show answer
Correct Option: B

A string of a simple pendulum can bear maximum tension that is $1.5$ times the weight of the bob. What is the maximum angle with which it can oscillate?

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $\cos^{-1} (0)$

  2. $\cos^{-1} (0.75)$

  3. $\cos^{-1} (0.25)$

  4. $\cos^{-1} (\sqrt {3}/2)$

Show answer
Correct Option: A

A simple pendulum with a metal bob has a time period $T$. Now the bob is immersed in a liquid which is non viscous. This time the time period is $4T$. The the ratio of densities of metal bpob and that of the liquid is

angular simple harmonic motion example of simple harmonic motion oscillatory motion oscillations physics

  1. $15:16$

  2. $16:15$

  3. $1:16$

  4. $16:1$

Show answer
Correct Option: C