Tag: oscillatory motion

Quizzes (7) Questions (124)

Questions Related to oscillatory motion

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

  1. $\phi _A = \phi _B = \phi _c$
  2. $\phi _A < \phi _B = 0 < \phi _c$
  3. $\phi _A > \phi _B = 0 > \phi _c$
  4. $\phi _A > \phi _B > 0 > \phi _c$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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:

  1. $400 Hz$
  2. $100 Hz$
  3. $256 Hz$
  4. $200 Hz$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The fundamental frequency of a stretched string is given by f = (1/2L) * sqrt(T/mu). Given L = 1 m, mass m = 5 x 10^-4 kg so linear mass density mu = 5 x 10^-4 kg/m, and tension T = 20 N. Plugging these in yields f = (1/2) * sqrt(20 / (5 x 10^-4)) = (1/2) * sqrt(40000) = (1/2) * 200 = 100 Hz.

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

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):

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

  2. 2
  3. $5\sqrt {10} $
  4. $\frac{1}{{5\sqrt {10} }}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation is d^2x/dt^2 + pi^2 * x = 0. Comparing to d^2x/dt^2 + w^2 * x = 0, we get w^2 = pi^2, so w = pi. Since w = 2 * pi * f, then pi = 2 * pi * f, which gives f = 1/2 Hz.

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

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

  1. simple pendulum

  2. torsional pendulum

  3. compound pendulum

  4. seconds pendulum
Reveal answer Fill a bubble to check yourself
C Correct answer
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)