For a particle of mass m executing SHM with angular frequency ω , the kinetic energy k is given by k=k0cos2 ω t . The equation of its displacement can be

Question

For a particle of mass m executing SHM with angular frequency ω , the kinetic energy k is given by k=k0cos2 ω t . The equation of its displacement can be (A) ((k0/m ω2))1 / 2 sin ω t (B) ((2 k0/m ω2))1 / 2 sin ω t (C) ((2 ω2/m k0))1 / 2 sin ω t (D) ((2 k0/m ω))1 / 2 sin ω t

Tardigrade Admin · Accepted Answer

If m is the mass, r is the amplitude of oscillation, then maximum kinetic energy, k0=(1/2) m ω2 r2 or r=((2 k0/m ω2))(1/2) The displacement equation can be y=r sin ω t=((2 k0/m ω2))(1/2) sin ω t

Q. For a particle of mass $m$ executing SHM with angular frequency $ω$ , the kinetic energy $k$ is given by $k = k_{0} co s^{2} ω t .$ The equation of its displacement can be

$(\frac{k _{0}}{m ω ^{2}})^{1/2} sin ω t$

$(\frac{2 k _{0}}{m ω ^{2}})^{1/2} sin ω t$

$(\frac{2 ω ^{2}}{m k _{0}})^{1/2} sin ω t$

$(\frac{2 k _{0}}{mω})^{1/2} sin ω t$

If $m$ is the mass, $r$ is the amplitude of oscillation, then maximum kinetic energy,
$k_{0} = \frac{1}{2} m ω^{2} r^{2}$ or $r = (\frac{2 k _{0}}{m ω ^{2}})^{\frac{1}{2}}$
The displacement equation can be $y = r sin ω t = (\frac{2 k _{0}}{m ω ^{2}})^{\frac{1}{2}} sin ω t$

Q. For a particle of mass m executing SHM with angular frequency ω , the kinetic energy k is given by k=k0​cos2ωt. The equation of its displacement can be

(mω2k0​​)1/2sinωt

(mω22k0​​)1/2sinωt

(mk0​2ω2​)1/2sinωt