Tag: angular simple harmonic motion

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Questions Related to angular simple harmonic motion

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

A metallic disc oscillates about an axis through its edge in it's own plane. The equivalent length of the disc as a pendulum is

  1. $r$
  2. $\dfrac r3$
  3. $\dfrac { r } { 2 }$
  4. $\dfrac { 3r } { 2 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a disc pivoted at its edge, I = I_cm + mR^2 = (1/2)mR^2 + mR^2 = (3/2)mR^2. The equivalent length L_eq = I/(mR) = (3/2)R.

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

The bob of a simple pendulum executes  $S H M$  in water with a period  $t,$  while the period of oscillation of the bob is  $t _{ 0 }$  in air. Neglecting the frictional force of water and given that the density of the bob is  $( 4 / 3 ) \times 1000 kg / { m } ^ { 3 }.$  What relationship between  $t$  and  $t _ { 0 }$  is true ?

  1. $t = t _ { 0 }$
  2. $t = 4 t _ { 0 }$
  3. $t = 2 t _ { 0 }$
  4. $t = t _ { 0 } / 2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The effective gravity in water is g' = g(1 - rho_water/rho_bob). Given rho_bob = 4/3 * 1000 and rho_water = 1000, g' = g(1 - 3/4) = g/4. Since T is proportional to 1/sqrt(g), T_water = T_air / sqrt(1/4) = 2 * T_air.

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

A simple pendulum is released when $\theta = \pi/6$. The time period of oscillation is

  1. $\displaystyle 2\pi\sqrt{\frac{l}{g}}$
  2. $\displaystyle 2\pi\sqrt{\frac{l}{g}}\left(\frac{293}{288}\right)$
  3. $\displaystyle 2\pi\sqrt{\frac{l}{g}}\left(\frac{288}{293}\right)$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For large amplitudes, the time period is given by 
$T={2\pi }{\sqrt{\dfrac{L}{g}}}(1+\dfrac{\theta ^{2}}{16})$
Substitute $\theta =\dfrac{\pi }{6}$, we get answer as 
$T={2\pi }{\sqrt{\dfrac{L}{g}}}(\dfrac{293}{288})$
Option B is correct.

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

A pendulum suspended from the ceiling of an elevator at rest has time period ${ T } _{ 1 }$. When the elevator moves up with an acceleration 'a' its time period of oscillation becomes ${ T } _{ 2 }$ when the elevator moves down with an acceleration 'a', its period of oscillation become ${ T } _{ 3 }$ then

  1. ${ T } _{ 1 }=\sqrt { { T } _{ 2 }{ T } _{ 3 } } $
  2. ${ T } _{ 1 }=\sqrt { T _{ 2 }{ ^{ 2 }T _{ 3 } }^{ 2 } } $
  3. ${ T } _{ 1 }=\dfrac { \sqrt { 2 } { T } _{ 2 }{ T } _{ 3 } }{ \sqrt { {T _{ 2 }}^{ 2 }+{T _{ 3 } }^{ 2 } } } $
  4. ${ T } _{ 1 }=\dfrac { { T } _{ 2 }{ T } _{ 3 } }{ \sqrt { {T _{ 2 }}^{ 2 }+{T _{ 3 } }^{ 2 } } } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

T1 = 2*pi*sqrt(l/g). T2 = 2*pi*sqrt(l/(g+a)). T3 = 2*pi*sqrt(l/(g-a)). Thus, 1/T2^2 = (g+a)/(4*pi^2*l) and 1/T3^2 = (g-a)/(4*pi^2*l). Adding these gives 1/T2^2 + 1/T3^2 = 2g/(4*pi^2*l) = 2/T1^2. Solving for T1 gives T1 = sqrt(2)*T2*T3 / sqrt(T2^2 + T3^2).

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

In a conical pendulum, when the bob moves in a horizontal circle of radius r, with uniform speed V, the string of length L describe a cone of semi-vertical angle $\theta$. The tension  in the string is given by 

  1. $T = \dfrac{mgl}{(L^2 - r^2)}$
  2. $ T = \dfrac{\sqrt {L^2 - r^2}}{mgl}$
  3. $ T = \dfrac{mgL}{\sqrt {L^2 - r^2}}$
  4. $ T = \dfrac{mgL}{(L^2 - r^2)^2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a conical pendulum, T*cos(theta) = mg. From the geometry, cos(theta) = h/L = sqrt(L^2 - r^2)/L. Therefore, T = mg/cos(theta) = mgL / sqrt(L^2 - r^2).

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

A simple pendulum in which the bob swings in a horizontal circle is called.

  1. Compound pendulum

  2. Horizontal pendulum

  3. Conical pendulum

  4. Gallitzin pendulum
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A conical pendulum consists of a weight (bob) fixed to the end of a string suspended from a pivot, where the bob moves in a horizontal circle at a constant speed.