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Instantaneous Rate of Change

9. The time p...

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9. The time period of a particle executing simple hermonic motion is T,if the time is calculated from the mean position then what will be the time taken by the particle to cover the distance from the mean position to the mid-point of extreme position?

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Q. A particle executing simple harmonic motion has a period of

6 s

. The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is

Q. The time taken by a particle executing simple harmonic motion of time period T to move from the mean position to half the maximum displacement is

Q. The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is
(a) the mean position
(b) an extreme position
(c) between the mean position and the positive extreme
(d) between the mean position and the negative extreme

Q. A particle executes a simple harmonic motion of time period

T

. Find the time taken by the particle to go directly from its mean position to half the amplitude.

Q. Assertion :In simple harmonic motion A is the amplitude of oscillation. If

t_{1}

be the time to reach the particle from mean position to

\frac{A}{\sqrt{2}}

t_{2}

the time to reach from

\frac{A}{\sqrt{2}}

t_{1} = \frac{t_{2}}{\sqrt{2}}

Reason : Equation of motion for the particle starting from mean position is given by

x = A c o s (ω t)

and of the particle starting from extreme position is given by

A s i n (ω t)

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