For a particle executing SHM, the kinetic energy K is given by K=K0 cos 2 ω t . The equation of its displacement can be

Question

For a particle executing SHM, the kinetic energy K is given by K=K0 cos 2 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 and r is the amplitude of oscillation, then maximum kinetic energy, or K0 =(1/2) m ω2 r2 r =((2 K0/m ω2))1 / 2 The displacement equation can be y=r sin ω t=((2 K0/m ω))1 / 2 sin ω t

Q. For a particle executing SHM, the kinetic energy $K$ is given by $K = K_{0} cos^{2} ω t .$ 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 and $r$ is the amplitude of oscillation, then maximum kinetic energy,
or $K_{0} = \frac{1}{2} m ω^{2} r^{2}$
$r = (\frac{2 K _{0}}{m ω ^{2}})^{1/2}$
The displacement equation can be
$y = r sin ω t = (\frac{2 K _{0}}{mω})^{1/2} sin ω t$

Q. For a particle executing SHM, 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