Tag: damped harmonic motion

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Questions Related to damped harmonic motion

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

The amplitude of a damped oscilator becomes one-half after $t$ second. If the amplitude becomes $\dfrac {1}{n}$ after $3t$, second, then $n$ is equal to

  1. $\dfrac {1}{8}$
  2. $8$
  3. $\dfrac {1}{4}$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Amplitude A(t) = A0 * e^(-bt). Given A(t) = A0/2, e^(-bt) = 1/2. For 3t, A(3t) = A0 * (e^(-bt))^3 = A0 * (1/2)^3 = A0/8. Thus, n = 8.

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

A system is executing forced harmonic resonant oscillations. The work done by the external driving force

  1. is equal to maximum K.E.

  2. is equal to maximum P.E.

  3. is equal to total energy

  4. is dissipated by damping forces
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Generally, work done by external force goes to total energy of the system. But in forced oscillations, it is dissipated by damping forces.

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

Equation of motion for a particle performing damped harmonic oscillation is given as $x = e^{-1 t} cos (10 \pi t + \phi)$. The times when amplitude will half of the initial is :

  1. $27$
  2. $4$
  3. $1$
  4. $7$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\dfrac{A _0}{2} = A _0 e^{-0.1t} \Rightarrow e^{-0.1t} = 2 \Rightarrow 0.1t = \ell n 2$
$t = \dfrac{\ell n 2}{0.1} = 10 \, \ell n2 \approx 6.93 \approx 7s$

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

A particle is performing damped oscillation with frequency $5Hz$. After every $10$ oscillations its amplitude becomes half. find time from beginning after which the amplitude becomes $\dfrac{1}{1000}$ of its initial amplitude:

  1. $10 \,s$
  2. $20 \,s$
  3. $25 \,s$
  4. $50 \,s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$f = 5$
so $T = \dfrac{1}{5}$

$10T = \dfrac{10}{5} = 2$

$\dfrac{A _0}{1000} = A _0 \left(\dfrac{1}{2}\right)^{t/2}$

$(2)^{t/2} = 1000$

$\left(\dfrac{t}{2}\right) log 2 = 3$

$t = \dfrac{6}{log 2} \approx 20 s$

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

The frequency of vibration is less than the natural frequency in

  1. Forced vibrations

  2. Free vibration

  3. Damped vibrations

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

It is our common experience that when a body is made to vibrate in a medium , the amplitude of the vibrating body continuously decreases with time and ultimately the body stops vibrating. This is called the damped vibrations.

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

A particle oscillating under a force $\bar{F} = - k \bar{x} - b \bar{v}$ is a (k and b are constants)

  1. simple harmonic oscillator

  2. linear oscillator

  3. damped oscillator

  4. forced oscillator
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A particle oscillating under a force $\bar{F} = - k \bar{x} - b \bar{v}$ is damped oscillator. The first term $-k \bar{x}$ represents the restoring force and second term $-b \bar{v}$ represents the damping force.