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Q.

A particle perfroms SHM with a period T and amplitude a. The mean velocity of the particle over the time interval during which it travels a distance a/2 from the extreme position is

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a

a/T

b

2a/T

c

3a/T

d

a/2T

answer is C.

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Detailed Solution

x=acos⁡ωta/2=acos⁡ωt0 or  cos⁡π3=cos⁡ωt0  or  π3=ωt0 ∴t0=π3ω v=dxdt=−aωsin⁡ωt∴ v¯=∫0π/3ω vdt∫0π/3ω dt But  ω=2πT ∴ v¯=3aT
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A particle perfroms SHM with a period T and amplitude a. The mean velocity of the particle over the time interval during which it travels a distance a/2 from the extreme position is