Question #213149

What is displacement of an object in Simple Harmonic Motion when kinetic and potential energy are equal? please explain


1
Expert's answer
2021-07-05T08:43:27-0400

E=Ek+EpE = E_k+E_p

Ek=mv22E_k =\frac{mv^2}{2}

Ep=kx22E_p =\frac{kx^2}{2}

where x offset from equilibrium point position\text{where x offset from equilibrium point position}

let A oscillation amplitude,then for x = A:\text{let A oscillation amplitude,then for x = A:}

E=Ek+EpE=E'_k+E'_p

Ek=0 etc v=0E'_k= 0 \text{ etc }v= 0

Ep=kA22E_p =\frac{kA^2}{2}

E=kA22E = \frac{kA^2}{2}

if Ep=Ek:\text{if } E_p=E_k:

Ep+Ek=E;E_p+E_k= E;

2Ep=kA222*E_p=\frac{kA^2}{2}

2kx122=kA222*\frac{kx_1^2}{2}=\frac{kA^2}{2}

x1=A22=0.71Ax_1= \sqrt{\frac{A^2}{2}}=0.71*A

Answer: kinetic and potential energies are equal when shifted \text{Answer: kinetic and potential energies are equal when shifted }

by 0.71*A from the equilibrium point;\text {by 0.71*A from the equilibrium point;}

 A this is the Simple Harmonic Motion amplitude\text{ A this is the Simple Harmonic Motion amplitude}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS