The velocity `v` of a particle of mass is moving along a straight line change with time `t` as `(d^(2)v)/(dt^(2)) = - Kv` where `K` is a particle constant which of the following statement is correct?A. the particle does not perform SHM.B. The particle performs SHM with time period `2pisqrt((m)/(K))`C. The particle performs SHM with frequency `(sqrtK)/(2pi)`D. The particle performs SHM with time period `(2pi)/(K)`.

The velocity `v` of a particle of mass is moving along a straight line

1.	The velocity `v` of a particle of mass is moving along a straight line change with time `t` as `(d^(2)v)/(dt^(2)) = - Kv` where `K` is a particle constant which of the following statement is correct?A. the particle does not perform SHM.B. The particle performs SHM with time period `2pisqrt((m)/(K))`C. The particle performs SHM with frequency `(sqrtK)/(2pi)`D. The particle performs SHM with time period `(2pi)/(K)`.
Answer» Correct Answer - C `(d^2v)/(dt)=-kv^2` This equation has standard solution `v=v_0sin(sqrtkt+theta)`, where `omega=sqrtk` hence the particle executes SHM with angular frequency `omega=sqrtk` or frequency `f=(sqrtk)/(2pi)`

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