The displacement x of a particle varies with time t as, $x = {ae}^{- αt} + b e^{βt}$ where a, b α and β are positive constants. The velocity of the particle will

go on decreasing with time

be independent of $α and β$

drop to zero when $α = β$

go on increasing with time

Solution

go on increasing with time

$x = a e^{αt} + b e^{βt} So velocity v = \frac{dX}{dt} = - a {αe}^{- αt} + b {βe}^{βe} ν = A + B Where A = - a {αe}^{- αt}, B = b {βe}^{βr}$

The value of term $A = a e^{- αt}$ decreases and of term $B = b {βe}^{βe}$ increases with increase in time. As a result, velocity goes on increasing with time.

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The displacement x of a particle varies with time t as, $x = {ae}^{- αt} + b e^{βt}$ where a, b α and β are positive constants. The velocity of the particle will

go on decreasing with time

be independent of $α and β$

drop to zero when $α = β$

go on increasing with time

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A particle of mass m executes simple harmonic motion with amplitude ‘a’ and frequency ‘ν’. The average kinetic energy during its motion from the position of equilibrium to the end is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

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The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

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For Daily Free Study Material Join wiredfaculty

Oscillations

The displacement x of a particle varies with time t as, x = ae-αt +b e βt where a, b α and β are positive constants. The velocity of the particle will go on decreasing with time be independent of α and β drop to zero when α = β go on increasing with time

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A particle of mass m executes simple harmonic motion with amplitude ‘a’ and frequency ‘ν’. The average kinetic energy during its motion from the position of equilibrium to the end is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

The function sin2(ωt) represents

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The displacement x of a particle varies with time t as, $x = {ae}^{- αt} + b e^{βt}$ where a, b α and β are positive constants. The velocity of the particle will

go on decreasing with time

be independent of $α and β$

drop to zero when $α = β$

go on increasing with time

The function sin²(ωt) represents