Class 11PhysicsOscillationsDifferent types of oscillations (Free, Damped, Forced Oscillation and Resonance)
Difficult$A$ block of mass $1 \, kg$ attached to a spring is made to oscillate with an initial amplitude of $12 \, cm$. After $2 \, minutes$ the amplitude decreases to $6 \, cm$. Determine the value of the damping constant $b$ for this motion. (Take $\ln 2 = 0.693$)
- A$0.69 \times 10^{-2} \, kg \, s^{-1}$
- B$3.3 \times 10^{-2} \, kg \, s^{-1}$
- C$5.7 \times 10^{-3} \, kg \, s^{-1}$
- D$1.16 \times 10^{-2} \, kg \, s^{-1}$
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Similar Questions
$Assertion :$ The amplitude of an oscillating pendulum decreases gradually with time.
$Reason :$ The frequency of the pendulum decreases with time.
$Reason :$ The frequency of the pendulum decreases with time.
The time taken for the amplitude of vibrations of a damped oscillator to drop to $25 \%$ of its initial value is $t$. The time taken for its mechanical energy to drop to $50 \%$ of its initial mechanical energy is
DifficultAP EAMCET 2023
View Solution$A$ spring-mass system executes damped harmonic oscillations given by the equation $y = A e^{-\frac{bt}{2m}} \sin(\omega' t + \phi)$,where the symbols have their usual meanings. If a $2 \ kg$ mass $(m)$ is attached to a spring of force constant $(K) = 1250 \ N/m$,the period of the oscillation is $(\pi / 12) \ s$. The damping constant $b$ has the value ..... $kg/s$.
Medium
View SolutionFor the damped oscillator shown in the figure,the mass $m$ of the block is $200 \; g$,$k = 90 \; N m^{-1}$,and the damping constant $b$ is $40 \; g s^{-1}$. Calculate:
$(a)$ the period of oscillation,
$(b)$ the time taken for its amplitude of vibrations to drop to half of its initial value,and
$(c)$ the time taken for its mechanical energy to drop to half its initial value.
$(a)$ the period of oscillation,
$(b)$ the time taken for its amplitude of vibrations to drop to half of its initial value,and
$(c)$ the time taken for its mechanical energy to drop to half its initial value.
Difficult
View Solution$A$ particle is performing simple harmonic motion. If the oscillations are damped oscillations,then the angular frequency is given by:
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