Tag: oscillatory motion

Questions Related to oscillatory motion

Three similar oscillators, A, B, C have the same small damping constant $r$, but different natural frequencies $\omega _0 = (k/m)^{\frac{1}{2}} : 1200 Hz, 1800 Hz, 2400 Hz$. If all three are driven by the same source at $1800 Hz$, which statement is correct for the phases of the velocities of the three?

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

  1. $\phi _A = \phi _B = \phi _c$

  2. $\phi _A < \phi _B = 0 < \phi _c$

  3. $\phi _A > \phi _B = 0 > \phi _c$

  4. $\phi _A > \phi _B > 0 > \phi _c$

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Correct Option: A
Explanation:

$tan \phi = \dfrac{\omega L- \dfrac{1}{\omega C}}{R}$

If $\omega < \omega _0 \Longrightarrow$ circuit is capacitive

$\Longrightarrow$ it leads voltage
$\Longrightarrow$ velocity leads force.
if $\omega = \omega _0 \phi = 0$
if $\omega > {\omega} _0$ velocity lags behind force.

A stretched string of one meter length, fixed at both the ends having mass of $5 \times 10^{-4}$ kg is under tension of 20 N. It is plucked at a point situated 25 cm from one end. The stretched string would vibrate with the frequency of:

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

  1. $400 Hz$

  2. $100 Hz$

  3. $256 Hz$

  4. $200 Hz$

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Correct Option: D

The equation of motion of a particle of mass $1$ g is $\frac{{{d^2}x}}{{d{t^2}}} + {\pi ^2}x = 0$ where $x$ is displacement (in m) from mean position. The frequency of oscillation is ( in Hz):

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

  1. $\frac{1}{2}$

  2. 2

  3. $5\sqrt {10} $

  4. $\frac{1}{{5\sqrt {10} }}$

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Correct Option: A

When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of the force of gravity, the body is known as

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

  1. simple pendulum

  2. torsional pendulum

  3. compound pendulum

  4. seconds pendulum

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Correct Option: C
Explanation:

When a rigid body is suspended vertically, and it oscillates with a small amplitude under the action of the force of gravity, the body is known as compound pendulum. Thus the periodic time of a compound pendulum is minimum when the distance between the point of suspension and the centre of gravity is equal to the radius of gyration of the body about its centre of gravity.

The correct option is (c)